OFFSET
1,1
COMMENTS
Named after the British mathematician Denis A. Higgs (1932-2011). - Amiram Eldar, Jun 05 2021
No prime of the form a*b^k + 1 (those in A089200) with a > 0, b > 1 and k > 2 is a Higgs's prime. - Mauro Fiorentini, Aug 08 2023
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Stanley Burris and Simon Lee, Tarski's high school identities, Amer. Math. Monthly, Vol. 100, No. 3 (1993), pp. 231-236.
Robert G. Wilson v, Note to N. J. A. Sloane with attachment, (Annotated scanned copy of The Am. Math. Mo. Vol. 100 No. 3 pp. 233, Mar. 1993).
Robert G. Wilson v, Letter to N. J. A. Sloane, Oct. 1993
MAPLE
a:=[2]; P:=1; j:=1;
for n from 2 to 32 do
P:=P*a[n-1]^2;
for i from j+1 to 250 do
if (P mod (ithprime(i)-1)) = 0 then
a:=[op(a), ithprime(i)]; j:=i; break; fi;
od:
od:
a; # N. J. A. Sloane, Feb 12 2017
MATHEMATICA
f[ n_List ] := (a = n; b = Apply[ Times, a^2 ]; d = NextPrime[ a[ [ -1 ] ] ]; While[ ! IntegerQ[ b/(d - 1) ] || d > b, d = NextPrime[ d ] ]; AppendTo[ a, d ]; Return[ a ]); Nest[ f, {2}, 75 ]
nxt[{p_, a_}]:=Module[{np=NextPrime[a]}, While[PowerMod[p, 2, np-1] != 0, np = NextPrime[np]]; {p*np, np}]; NestList[nxt, {2, 2}, 60][[All, 2]] (* Harvey P. Dale, Jul 09 2021 *)
PROG
(Haskell)
a007459 n = a007459_list !! (n-1)
a007459_list = f 1 a000040_list where
f q (p:ps) = if mod q (p - 1) == 0 then p : f (q * p ^ 2) ps else f q ps
-- Reinhard Zumkeller, Apr 14 2013
(PARI) step(v)=my(N=vecprod(v)^2); forprime(p=v[#v]+1, , if(N%(p-1)==0, return(concat(v, p))))
first(n)=my(v=[2]); for(i=2, n, v=step(v)); v \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from David W. Wilson
Definition clarified by N. J. A. Sloane, Feb 12 2017
STATUS
approved