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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 28 18:31 EDT 2021. Contains 346335 sequences. (Running on oeis4.)