

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
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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)unitrier.de), May 04 2004
More terms from David Wasserman, Jul 25 2005


STATUS

approved



