cp's OEIS Frontend

A088125 Let f(n,x) = 1 + 4*x + 6*x^2 + 8*x^3 + 9*x^4 + ... + composite(n)*x^n; a(n) = smallest x such that f(n,x) is a prime, or 0 if no such prime exists.

%I A088125 #18 Jul 02 2018 03:07:51
%S A088125 1,1,1,2,6,34,2,1,3,1,11,42,120,12,8,1,4,2,24,86,1,54,154,202,246,25,
%T A088125 10,60,1,114,34,22,21,1,88,14,276,70,795,518,448,252,6,2,1,18,768,124,
%U A088125 1,186,143,1,138,456,366,19,47,112,336,772,140,3,88,30,188,90,437,90,294
%N A088125 Let f(n,x) = 1 + 4*x + 6*x^2 + 8*x^3 + 9*x^4 + ... + composite(n)*x^n; a(n) = smallest x such that f(n,x) is a prime, or 0 if no such prime exists.
%C A088125 According to Bunyakovsky's conjecture, if f(n,X) is irreducible over the rationals, f(n,x) is prime for infinitely many positive integers x. It is irreducible for 1 <= n <= 1800. - _Robert Israel_, Jul 01 2018
%H A088125 Robert Israel, <a href="/A088125/b088125.txt">Table of n, a(n) for n = 1..400</a>
%H A088125 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bunyakovsky_conjecture">Bunyakovsky conjecture</a>
%p A088125 P:= 1: q:= 1:
%p A088125 for n from 1 to 100 do
%p A088125   q:= q+1;
%p A088125   while isprime(q) do q:= q+1 od;
%p A088125   P:= P + q*x^n;
%p A088125   if not irreduc(P) then A[n]:= 0
%p A088125   else
%p A088125     Pf:= unapply(P,x);
%p A088125     for xx from 1 while not isprime(Pf(xx)) do od:
%p A088125     A[n]:= xx;
%p A088125   fi
%p A088125 od:
%p A088125 seq(A[n],n=1..100); # _Robert Israel_, Jul 01 2018
%Y A088125 Cf. A088122, A088123, A088124.
%Y A088125 Cf. A060697 (n for which a(n)=1).
%K A088125 nonn
%O A088125 1,4
%A A088125 _Amarnath Murthy_, Sep 25 2003
%E A088125 More terms from Tom Mueller (muel4503(AT)uni-trier.de), May 04 2004
%E A088125 More terms from _David Wasserman_, Jul 25 2005