# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a001608 Showing 1-1 of 1 %I A001608 M0429 N0163 #438 Nov 05 2024 08:11:02 %S A001608 3,0,2,3,2,5,5,7,10,12,17,22,29,39,51,68,90,119,158,209,277,367,486, %T A001608 644,853,1130,1497,1983,2627,3480,4610,6107,8090,10717,14197,18807, %U A001608 24914,33004,43721,57918,76725,101639,134643,178364,236282,313007 %N A001608 Perrin sequence (or Ondrej Such sequence): a(n) = a(n-2) + a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2. %C A001608 Has been called the skiponacci sequence or skiponacci numbers. - _N. J. A. Sloane_, May 24 2013 %C A001608 For n >= 3, also the numbers of maximal independent vertex sets, maximal matchings, minimal edge covers, and minimal vertex covers in the n-cycle graph C_n. - _Eric W. Weisstein_, Mar 30 2017 and Aug 03 2017 %C A001608 With the terms indexed as shown, has property that p prime => p divides a(p). The smallest composite n such that n divides a(n) is 521^2. For quotients a(p)/p, where p is prime, see A014981. %C A001608 Asymptotically, a(n) ~ r^n, with r=1.3247179572447... the inverse of the real root of 1-x^2-x^3=0 (see A060006). If n>9 then a(n)=round(r^n). - _Ralf Stephan_, Dec 13 2002 %C A001608 The recursion can be used to compute a(-n). The result is -A078712(n). - _T. D. Noe_, Oct 10 2006 %C A001608 For n>=3, a(n) is the number of maximal independent sets in a cycle of order n. - _Vincent Vatter_, Oct 24 2006 %C A001608 Pisano period lengths are given in A104217. - _R. J. Mathar_, Aug 10 2012 %C A001608 From _Roman Witula_, Feb 01 2013: (Start) %C A001608 Let r1, r2 and r3 denote the roots of x^3 - x - 1. Then the following identity holds: a(k*n) + (a(k))^n - (a(k) - r1^k)^n - (a(k) - r2^k)^n - (a(k) - r3^k)^n %C A001608 = 0 for n = 0, 1, 2, %C A001608 = 6 for n = 3, %C A001608 = 12*a(k) for n = 4, %C A001608 = 10*[2*(a(k))^2 - a(-k)] for n = 5, %C A001608 = 30*a(k)*[(a(k))^2 - a(-k)] for n = 6, %C A001608 = 7*[6*(a(k))^4 - 9*a(-k)*(a(k))^2 + 2*(a(-k))^2 - a(k)] for n = 7, %C A001608 = 56*a(k)*[((a(k))^2 - a(-k))^2 - a(k)/2] for n = 8, %C A001608 where a(-k) = -A078712(k) and the formula (5.40) from the paper of Witula and Slota is used. (End) %C A001608 The parity sequence of a(n) is periodic with period 7 and has the form (1,0,0,1,0,1,1). Hence we get that a(n) and a(2*n) are congruent modulo 2. Similarly we deduce that a(n) and a(3*n) are congruent modulo 3. Is it true that a(n) and a(p*n) are congruent modulo p for every prime p? - _Roman Witula_, Feb 09 2013 %C A001608 The trinomial x^3 - x - 1 divides the polynomial x^(3*n) - a(n)*x^(2*n) + ((a(n)^2 - a(2*n))/2)*x^n - 1 for every n>=1. For example, for n=3 we obtain the factorization x^9 - 3*x^6 + 2*x^3 - 1 = (x^3 - x - 1)*(x^6 + x^4 - 2*x^3 + x^2 - x + 1). Sketch of the proof: Let p,s,t be roots of the Perrin polynomial x^3 - x - 1. Then we have (a(n))^2 = (p^n + s^n + t^n)^2 = a(2*n) + 2*a(n)*x^n -2*x^n + 2/x^n for every x = p,s,t, i.e., x^(3*n) - a(n)*x^(2*n) + ((a(n)^2 - a(2*n))/2)*x^n - 1 = 0 for every x = p,s,t, which finishes the proof. By discussion of the power(a(n))^3 = (p^n + s^n + t^n)^3 it can be deduced that the trinomial x^3 - x - 1 divides the polynomial 2*x^(4*n) - a(n)*x^(3*n) - a(2*n)*x^(2*n) + ((a(n)^3 - a(3*n) - 3)/3)*x^n - a(n) = 0. Co-author of these divisibility relations is also my young student Szymon Gorczyca (13 years old as of 2013). - _Roman Witula_, Feb 09 2013 %C A001608 The sum of powers of the real root and complex roots of x^3-x-1=0 as expressed as powers of the plastic number r, (see A060006). Let r0=1, r1=r, r2=1+r^(-1) and c0=2, c1=-r and c3 = r^(-5) then a(n) = r(n-2)+r(n-3) + c(n-2)+c(n-3). Example: a(5) = 1 + r^(-1) + 1 + r + 2 - r + r^(-5) = 4 + r^(-1) + r^(-5) = 5. - _Richard Turk_, Jul 14 2016 %C A001608 Also the number of minimal total dominating sets in the n-sun graph. - _Eric W. Weisstein_, Apr 27 2018 %C A001608 Named after the French engineer François Olivier Raoul Perrin (1841-1910). - _Amiram Eldar_, Jun 05 2021 %C A001608 a(p) = p*A127687(p) for p prime. - _Robert FERREOL_, Apr 09 2024 %D A001608 Olivier Bordellès, Thèmes d'Arithmétique, Ellipses, 2006, Exercice 4.11, p. 127.0 %D A001608 Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.2.2. %D A001608 Dmitry Fomin, On the properties of a certain recursive sequence, Mathematics and Informatics Quarterly, Vol. 3 (1993), pp. 50-53. %D A001608 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 70. %D A001608 Manfred Schroeder, Number Theory in Science and Communication, 3rd ed., Springer, 1997. %D A001608 A. G. Shannon, P. G. Anderson and A. F. Horadam, Properties of Cordonnier, Perrin and Van der Laan numbers, International Journal of Mathematical Education in Science and Technology, Volume 37:7 (2006), 825-831. See Q_n. %D A001608 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A001608 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A001608 Indranil Ghosh, Table of n, a(n) for n = 0..8172 (terms 0..1000 from T. D. Noe) %H A001608 William Adams and Daniel Shanks, Strong primality tests that are not sufficient, Math. Comp., Vol. 39, No. 159 (1982), pp. 255-300. %H A001608 Kouèssi Norbert Adédji, Japhet Odjoumani, and Alain Togbé, Padovan and Perrin numbers as products of two generalized Lucas numbers, Archivum Mathematicum, Vol. 59 (2023), No. 4, 315-337. %H A001608 Bill Amend, "Foxtrot" cartoon, Oct 11, 2005 (Illustration of initial terms! From www.ucomics.com/foxtrot/.) %H A001608 Mohamadou Bachabi and Alain S. Togbé, Products of Fermat or Mersenne numbers in some sequences, Math. Comm. (2024) Vol. 29, 265-285. %H A001608 Herbert Batte, Taboka P. Chalebgwa and Mahadi Ddamulira, Perrin numbers that are concatenations of two distinct repdigits, arXiv:2105.08515 [math.NT], 2021. %H A001608 Daniel Birmajer, Juan B. Gil and Michael D. Weiner, Linear recurrence sequences with indices in arithmetic progression and their sums, arXiv:1505.06339 [math.NT], 2015. %H A001608 Eric Fernando Bravo, On concatenations of Padovan and Perrin numbers, Math. Commun. (2023) Vol 28, 105-119. %H A001608 Kevin S. Brown, Perrin's Sequence %H A001608 J. Chick, Problem 81G, Math. Gazette, Vol. 81, No. 491 (1997), p. 304. %H A001608 Tomislav Doslic and I. Zubac, Counting maximal matchings in linear polymers, Ars Mathematica Contemporanea, Vol. 11 (2016), pp. 255-276. %H A001608 Robert Dougherty-Bliss, The Meta-C-finite Ansatz, arXiv preprint arXiv:2206.14852 [math.CO], 2022. %H A001608 Robert Dougherty-Bliss, Experimental Methods in Number Theory and Combinatorics, Ph. D. Dissertation, Rutgers Univ. (2024). See p. 34. %H A001608 Robert Dougherty-Bliss and Doron Zeilberger, Lots and Lots of Perrin-Type Primality Tests and Their Pseudo-Primes, arXiv:2307.16069 [math.NT], 2023. %H A001608 E. B. Escott, Problem 151, Amer. Math. Monthly, Vol. 15, No. 11 (1908), p. 209. %H A001608 Daniel C. Fielder, Special integer sequences controlled by three parameters, Fibonacci Quarterly, Vol. 6 (1968), pp. 64-70. %H A001608 Daniel C. Fielder, Errata:Special integer sequences controlled by three parameters, Fibonacci Quarterly, Vol. 6 (1968), pp. 64-70. %H A001608 Zoltán Füredi, The number of maximal independent sets in connected graphs, J. Graph Theory, Vol. 11, No. 4 (1987), pp. 463-470. %H A001608 Bill Gasarch, When does n divide a_n in this sequence? (2016). %H A001608 A. Justin Gopinath and B. Nithya, Mathematical and Simulation Analysis of Contention Resolution Mechanism for IEEE 802.11 ah Networks, Computer Communications (2018) Vol. 124, 87-100. %H A001608 Christian Holzbaur, Perrin pseudoprimes [Original link broke many years ago. This is a cached copy from the WayBack machine, dated Apr 24 2006] %H A001608 Dmitry I. Ignatov, On the Maximal Independence Polynomial of the Covering Graph of the Hypercube up to n = 6, Int'l Conf. Formal Concept Analysis, 2023. %H A001608 Stanislav Jakubec and Karol Nemoga, On a conjecture concerning sequences of the third order, Mathematica Slovaca, Vol. 36, No. 1 (1986), pp. 85-89. %H A001608 Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 90. %H A001608 Bir Kafle, Salah Eddine Rihane and Alain Togbé, A note on Mersenne Padovan and Perrin numbers, Notes on Num. Theory and Disc. Math., Vol. 27, No. 1 (2021), pp. 161-170. %H A001608 Vedran Krcadinac, A new generalization of the golden ratio, Fibonacci Quart., Vol. 44, No. 4 (2006), pp. 335-340. %H A001608 G. C. Kurtz, Daniel Shanks and H. C. Williams, Fast primality tests for numbers less than 50*10^9, Mathematics of Computation, Vol. 46, No. 174 (1986), pp. 691-701. [Studies primes in this sequence. - _N. J. A. Sloane_, Jul 28 2019] %H A001608 I. E. Leonard and A. C. F. Liu, A familiar recurrence occurs again, Amer. Math. Monthly, Vol. 119, No. 4 (2012), 333-336. %H A001608 J. M. Luck and A. Mehta, Universality in survivor distributions: Characterising the winners of competitive dynamics, Physical Review E, Vol. 92, No. 5 (2015), 052810; arXiv preprint, arXiv:1511.04340 [q-bio.QM], 2015. %H A001608 Matthew Macauley, Jon McCammond and Henning S. Mortveit, Dynamics groups of asynchronous cellular automata, Journal of Algebraic Combinatorics, Vol 33, No 1 (2011), pp. 11-35. %H A001608 Gregory Minton, Three approaches to a sequence problem, Math. Mag., Vol. 84, No. 1 (2011), pp. 33-37. %H A001608 Gregory T. Minton, Linear recurrence sequences satisfying congruence conditions, Proc. Amer. Math. Soc., Vol. 142, No. 7 (2014), pp. 2337-2352. MR3195758. %H A001608 B. H. Neumann and L. G. Wilson, Some Sequences like Fibonacci's, Fibonacci Quart., Vol. 17, No. 1 (1979), p. 83. %H A001608 Mathilde Noual, Dynamics of Circuits and Intersecting Circuits, in Language and Automata Theory and Applications, Lecture Notes in Computer Science, 2012, Volume 7183/2012, 433-444, DOI; also on arXiv, arXiv 1011.3930 [cs.DM], 2010. %H A001608 Ahmet Öteleş, Bipartite Graphs Associated with Pell, Mersenne and Perrin Numbers, An. Şt. Univ. Ovidius Constantą, (2019) Vol. 27, Issue 2, 109-120. %H A001608 R. Perrin, Query 1484, L'Intermédiaire des Mathématiciens, Vol. 6 (1899), p. 76. %H A001608 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009. %H A001608 Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992. %H A001608 Salah Eddine Rihane, Chèfiath Awero Adegbindin and Alain Togbé, Fermat Padovan And Perrin Numbers, J. Int. Seq., Vol. 23 (2020), Article 20.6.2. %H A001608 Salah Eddine Rihane and Alain Togbé, Repdigits as products of consecutive Padovan or Perrin numbers, Arab. J. Math. (2021). %H A001608 David E. Rush, Degree n Relatives of the Golden Ratio and Resultants of the Corresponding Polynomials, Fibonacci Quart., Vol. 50, No. 4 (2012), pp. 313-325. See p. 318. %H A001608 J. O. Shallit and J. P. Yamron, On linear recurrences and divisibility by primes, Fibonacci Quart., Vol. 22, No. 4 (1984), p. 366. %H A001608 Ian Stewart, Tales of a Neglected Number, Mathematical Recreations, Scientific American, Vol. 274, No. 6 (1996), pp. 102-103. %H A001608 Ondrej Such, An Insufficient Condition for Primality, Problem 10268, Amer. Math. Monthly, Vol. 102, No. 6 (1995), pp. 557-558. %H A001608 Ondrej Such, An Insufficient Condition for Primality, Problem 10268, Amer. Math. Monthly, Vol. 103, No. 10 (1996), p. 911. %H A001608 Pagdame Tiebekabe and Kouèssi Norbert Adédji, On Padovan or Perrin numbers as products of three repdigits in base delta, 2023. %H A001608 Razvan Tudoran, Problem 653, College Math. J., Vol. 31, No. 3 (2000), pp. 223-224. %H A001608 Vincent Vatter, Social distancing, primes, and Perrin numbers, Math Horiz., Vol. 29, No. 1, pp. 5-7. %H A001608 Stan Wagon, Letter to the Editor, Math. Mag., Vol. 84, No. 2 (2011), p. 119. %H A001608 Michel Waldschmidt, Lectures on Multiple Zeta Values, IMSC 2011. %H A001608 Eric Weisstein's World of Mathematics, Cycle Graph %H A001608 Eric Weisstein's World of Mathematics, Maximal Independent Edge Set %H A001608 Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set %H A001608 Eric Weisstein's World of Mathematics, Minimal Edge Cover. %H A001608 Eric Weisstein's World of Mathematics, Minimal Vertex Cover %H A001608 Eric Weisstein's World of Mathematics, Perrin Pseudoprime %H A001608 Eric Weisstein's World of Mathematics, Perrin Sequence %H A001608 Eric Weisstein's World of Mathematics, Sun Graph %H A001608 Eric Weisstein's World of Mathematics, Total Dominating Set %H A001608 Willem's Fibonacci site, Perrin and Fibonacci. %H A001608 Wikipedia, Perrin Number. %H A001608 Roman Witula and Damian Slota, Conjugate sequences in Fibonacci-Lucas sense and some identities for sums of powers of their elements, Integers, Vol. 7 (2007), #A08. %H A001608 Richard J. Yanco, Letter and Email to N. J. A. Sloane, 1994 %H A001608 Richard Yanco and Ansuman Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994. (Annotated scanned copy) %H A001608 Fatih Yilmaz and Durmus Bozkurt, Hessenberg matrices and the Pell and Perrin numbers, Journal of Number Theory, Volume 131, Issue 8 (August 2011), pp. 1390-1396. [The terms given in the paper contain a typo] %H A001608 Index entries for linear recurrences with constant coefficients, signature (0,1,1). %F A001608 G.f.: (3 - x^2)/(1 - x^2 - x^3). - _Simon Plouffe_ in his 1992 dissertation %F A001608 a(n) = r1^n + r2^n + r3^n where r1, r2, r3 are three roots of x^3-x-1=0. %F A001608 a(n-1) + a(n) + a(n+1) = a(n+4), a(n) - a(n-1) = a(n-5). - _Jon Perry_, Jun 05 2003 %F A001608 From _Gary W. Adamson_, Feb 01 2004: (Start) %F A001608 a(n) = trace(M^n) where M is the 3 X 3 matrix [0 1 0 / 0 0 1 / 1 1 0], the companion matrix of the characteristic polynomial of this sequence, P = X^3 - X - 1. %F A001608 M^n * [3, 0, 2] = [a(n), a(n+1), a(n+2)]; e.g., M^7 * [3, 0, 2] = [7, 10, 12]. %F A001608 a(n) = 2*A000931(n+3) + A000931(n). (End) %F A001608 a(n) = 3*p(n) - p(n-2) = 2*p(n) + p(n-3), with p(n) := A000931(n+3), n >= 0. - _Wolfdieter Lang_, Jun 21 2010 %F A001608 From _Francesco Daddi_, Aug 03 2011: (Start) %F A001608 a(0) + a(1) + a(2) + ... + a(n) = a(n+5) - 2. %F A001608 a(0) + a(2) + a(4) + ... + a(2*n) = a(2*n+3). %F A001608 a(1) + a(3) + a(5) + ... + a(2*n+1) = a(2*n+4) - 2. (End) %F A001608 From _Francesco Daddi_, Aug 04 2011: (Start) %F A001608 a(0) + a(3) + a(6) + a(9) + ... + a(3*n) = a(3*n+2) + 1. %F A001608 a(0) + a(5) + a(10) + a(15) + ... + a(5*n) = a(5*n+1)+3. %F A001608 a(0) + a(7) + a(14) + a(21) + ... + a(7*n) = (a(7*n) + a(7*n+1) + 3)/2. (End) %F A001608 a(n) = n*Sum_{k=1..floor(n/2)} binomial(k,n-2*k)/k, n > 0, a(0)=3. - _Vladimir Kruchinin_, Oct 21 2011 %F A001608 (a(n)^3)/2 + a(3n) - 3*a(n)*a(2n)/2 - 3 = 0. - _Richard Turk_, Apr 26 2017 %F A001608 2*a(4n) - 2*a(n) - 2*a(n)*a(3n) - a(2n)^2 + a(n)^2*a(2n) = 0. - _Richard Turk_, May 02 2017 %F A001608 a(n)^4 + 6*a(4n) - 4*a(3n)*a(n) - 3*a(2n)^2 - 12a(n) = 0. - _Richard Turk_, May 02 2017 %F A001608 a(n+5)^2 + a(n+1)^2 - a(n)^2 = a(2*(n+5)) + a(2*(n+1)) - a(2*n). - _Aleksander Bosek_, Mar 04 2019 %F A001608 From _Aleksander Bosek_, Mar 18 2019: (Start) %F A001608 a(n+12) = a(n) + 2*a(n+4) + a(n+11); %F A001608 a(n+16) = a(n) + 4*a(n+9) + a(n+13); %F A001608 a(n+18) = a(n) + 2*a(n+6) + 5*a(n+12); %F A001608 a(n+21) = a(n) + 2*a(n+12) + 6*a(n+14); %F A001608 a(n+27) = a(n) + 3*a(n+9) + 4*a(n+22). (End) %F A001608 a(n) = Sum_{j=0..floor((n-g)/(2*g))} 2*n/(n-2*(g-2)*j-(g-2)) * Hypergeometric2F1([-(n-2g*j-g)/2, -(2j+1)], [1], 1), g = 3 and n an odd integer. - _Richard Turk_, Oct 14 2019 %F A001608 E.g.f.: exp(r1*x) + exp(r2*x) + exp(r3*x), where r1, r2, r3 are three roots of x^3 - x - 1 = 0. - _Fabian Pereyra_, Nov 02 2024 %e A001608 From _Roman Witula_, Feb 01 2013: (Start) %e A001608 We note that if a + b + c = 0 then: %e A001608 1) a^3 + b^3 + c^3 = 3*a*b*c, %e A001608 2) a^4 + b^4 + c^4 = 2*((a^2 + b^2 + c^2)/2)^2, %e A001608 3) (a^5 + b^5 + c^5)/5 = (a^3 + b^3 + c^3)/3 * (a^2 + %e A001608 b^2 + c^2)/2, %e A001608 4) (a^7 + b^7 + c^7)/7 = (a^5 + b^5 + c^5)/5 * (a^2 + b^2 + c^2)/2 = 2*(a^3 + b^3 + c^3)/3 * (a^4 + b^4 + c^4)/4, %e A001608 5) (a^7 + b^7 + c^7)/7 * (a^3 + b^3 + c^3)/3 = ((a^5 + b^5 + c^5)/5)^2. %e A001608 Hence, by the Binet formula for a(n) we obtain the relations: a(3) = 3, a(4) = 2*(a(2)/2)^2 = 2, a(5)/5 = a(3)/3 * a(2)/2, i.e., a(5) = 5, and similarly that a(7) = 7. (End) %p A001608 A001608 :=proc(n) option remember; if n=0 then 3 elif n=1 then 0 elif n=2 then 2 else procname(n-2)+procname(n-3); fi; end proc; %p A001608 [seq(A001608(n),n=0..50)]; # _N. J. A. Sloane_, May 24 2013 %t A001608 LinearRecurrence[{0, 1, 1}, {3, 0, 2}, 50] (* _Harvey P. Dale_, Jun 26 2011 *) %t A001608 per = Solve[x^3 - x - 1 == 0, x]; f[n_] := Floor @ Re[N[ per[[1, -1, -1]]^n + per[[2, -1, -1]]^n + per[[3, -1, -1]]^n]]; Array[f, 46, 0] (* _Robert G. Wilson v_, Jun 29 2010 *) %t A001608 a[n_] := n*Sum[Binomial[k, n-2*k]/k, {k, 1, n/2}]; a[0]=3; Table[a[n] , {n, 0, 45}] (* _Jean-François Alcover_, Oct 04 2012, after _Vladimir Kruchinin_ *) %t A001608 CoefficientList[Series[(3 - x^2)/(1 - x^2 - x^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 03 2015 *) %t A001608 Table[RootSum[-1 - # + #^3 &, #^n &], {n, 0, 20}] (* _Eric W. Weisstein_, Mar 30 2017 *) %t A001608 RootSum[-1 - # + #^3 &, #^Range[0, 20] &] (* _Eric W. Weisstein_, Dec 30 2017 *) %o A001608 (PARI) a(n)=if(n<0,0,polsym(x^3-x-1,n)[n+1]) %o A001608 (PARI) A001608_list(n) = polsym(x^3-x-1,n) \\ _Joerg Arndt_, Mar 10 2019 %o A001608 (Haskell) %o A001608 a001608 n = a000931_list !! n %o A001608 a001608_list = 3 : 0 : 2 : zipWith (+) a001608_list (tail a001608_list) %o A001608 -- _Reinhard Zumkeller_, Feb 10 2011 %o A001608 (Python) %o A001608 A001608_list, a, b, c = [3, 0, 2], 3, 0, 2 %o A001608 for _ in range(100): %o A001608 a, b, c = b, c, a+b %o A001608 A001608_list.append(c) # _Chai Wah Wu_, Jan 27 2015 %o A001608 (GAP) a:=[3,0,2];; for n in [4..20] do a[n]:=a[n-2]+a[n-3]; od; a; # _Muniru A Asiru_, Jul 12 2018 %o A001608 (Magma) I:=[3,0,2]; [n le 3 select I[n] else Self(n-2) +Self(n-3): n in [1..50]]; // _G. C. Greubel_, Mar 18 2019 %o A001608 (Sage) ((3-x^2)/(1-x^2-x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 18 2019 %Y A001608 Closely related to A182097. %Y A001608 Cf. A000931, bisection A109377. %Y A001608 Cf. A013998 (Unrestricted Perrin pseudoprimes). %Y A001608 Cf. A018187 (Restricted Perrin pseudoprimes). %K A001608 nonn,easy,nice,changed %O A001608 0,1 %A A001608 _N. J. A. Sloane_ %E A001608 Additional comments from Mike Baker, Oct 11 2005 %E A001608 Definition edited by _Chai Wah Wu_, Jan 27 2015 %E A001608 Deleted certain dangerous or potentially dangerous links. - _N. J. A. Sloane_, Jan 30 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE