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.

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, 10, 60, 1, 114, 34, 22, 21, 1, 88, 14, 276, 70, 795, 518, 448, 252, 6, 2, 1, 18, 768, 124, 1, 186, 143, 1, 138, 456, 366, 19, 47, 112, 336, 772, 140, 3, 88, 30, 188, 90, 437, 90, 294

Offset

1,4

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..400

Wikipedia, Bunyakovsky conjecture

Maple

P:= 1: q:= 1:
for n from 1 to 100 do
  q:= q+1;
  while isprime(q) do q:= q+1 od;
  P:= P + q*x^n;
  if not irreduc(P) then A[n]:= 0
  else
    Pf:= unapply(P, x);
    for xx from 1 while not isprime(Pf(xx)) do od:
    A[n]:= xx;
  fi
od:
seq(A[n], n=1..100); # Robert Israel, Jul 01 2018

Crossrefs

Cf. A088122, A088123, A088124.

Cf. A060697 (n for which a(n)=1).

Sequence in context: A062970 A259436 A278611 * A064940 A105142 A227306

Adjacent sequences: A088122 A088123 A088124 * A088126 A088127 A088128

Keyword

nonn

Author

Amarnath Murthy, Sep 25 2003

Extensions

More terms from Tom Mueller (muel4503(AT)uni-trier.de), May 04 2004

More terms from David Wasserman, Jul 25 2005

Status

approved