# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a261354 Showing 1-1 of 1 %I A261354 #17 Aug 16 2015 12:07:21 %S A261354 31,191,541,809,1153,1301,2221,3037,3847,4049,4159,5441,8243,10177, %T A261354 12277,13681,14783,15619,17903,19463,20897,22697,24517,25163,25847, %U A261354 25849,26633,26647,27329,27407,28051,32653,35059,35747,36341,36527,37369,37811,38609,40949,42737,46679,51061,51607,54443,54679,56113,57637,60887,61493 %N A261354 Primes p such that prime(p)^2 - 2 = prime(q) for some prime q. %C A261354 Conjecture: The sequence has infinitely many terms. In general, for any integers a,b,c with a>0 and gcd(a,b,c)=1, if b^2-4*a*c is not a square, a+b+c is odd, and gcd(b,a+c) is not divisible by 3, then there are infinitely many prime pairs {p,q} such that a*prime(p)^2+b*prime(p)+c = prime(q). %D A261354 Zhi-Wei Sun, Problems on combinatorial properties of primes, in: M. Kaneko, S. Kanemitsu and J. Liu (eds.), Number Theory: Plowing and Starring through High Wave Forms, Proc. 7th China-Japan Seminar (Fukuoka, Oct. 28 - Nov. 1, 2013), Ser. Number Theory Appl., Vol. 11, World Sci., Singapore, 2015, pp. 169-187. %H A261354 Zhi-Wei Sun, Table of n, a(n) for n = 1..100 %H A261354 Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641 [math.NT], 2014. %e A261354 a(1) = 31 since 31 is a prime, and prime(31)^2-2 = 127^2-2 = 16127 = prime(1877) with 1877 prime. %t A261354 PQ[n_]:=PrimeQ[n]&&PrimeQ[PrimePi[n]] %t A261354 f[k_]:=Prime[Prime[k]]^2-2 %t A261354 n=0;Do[If[PQ[f[k]],n=n+1;Print[n," ",Prime[k]]],{k,1,6200}] %Y A261354 Cf. A000040, A049002, A062326, A237413, A260120, A261281, A261352, A261361. %K A261354 nonn %O A261354 1,1 %A A261354 _Zhi-Wei Sun_, Aug 15 2015 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE