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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.
2
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
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. A060697 (n for which a(n)=1).
Sequence in context: A062970 A259436 A278611 * A064940 A105142 A227306
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