A088122 -id:A088122 - cp's OEIS frontend

A088123 Let f(n,x) = 1 + 2x + 3x^2 + 5x^3 + 7x^4 + ... + prime(n)*x^n; a(n) = smallest value of x such that f(n,x) is a prime, or 0 if no such prime exists.

1, 2, 1, 6, 1, 6, 1, 8, 1, 74, 6, 6, 1, 2, 11, 102, 20, 88, 1, 52, 10, 18, 2, 56, 1, 26, 37, 216, 1, 78, 1, 28, 21, 160, 3, 276, 30, 1542, 42, 598, 20, 20, 333, 186, 8, 82, 11, 90, 1, 246, 1, 240, 83, 58, 9, 76, 1, 16, 21, 700, 60, 10, 87, 250, 62, 406, 2, 502, 140, 186, 1293, 578

Offset: 1

Amarnath Murthy, Sep 25 2003

nonn

			a(4) = 6 as, A088122(4) = 10273 = f(4,6).

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A088122.

Table[Clear[x,n,eq];eq=Total[Table[Prime[n]x^n,{n,t}]]+1;x=1; While[ !PrimeQ[ eq],x++];x,{t,80}] (* Harvey P. Dale, Apr 27 2013 *)

More terms from Tom Mueller, May 04 2004

More terms from David Wasserman, Jul 25 2005

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

Original entry on oeis.org

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

Amarnath Murthy, Sep 25 2003

nonn

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

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

Cf. A088122, A088123, A088124.

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

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

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

More terms from David Wasserman, Jul 25 2005

A088124 Let f(n,x) = 1 + 4x + 6x^2 + 8x^3 + 9x^4 + ... + composite(n)*x^n; a(n)= smallest prime f(n,x), or 0 if no such prime exists.

Original entry on oeis.org

5, 11, 19, 241, 91393, 19004355761, 3121, 79, 456151, 113, 6214345434133, 647380324484508990481, 23727240537882663031640150881, 33371196003273361, 998893713465761, 251, 610748560241, 14136113, 5228581733308860742493949409

Offset: 1

Amarnath Murthy, Sep 25 2003

nonn

Cf. A088122, A088123, A088125.

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

cp's OEIS Frontend

A088123 Let f(n,x) = 1 + 2x + 3x^2 + 5x^3 + 7x^4 + ... + prime(n)*x^n; a(n) = smallest value of x such that f(n,x) is a prime, or 0 if no such prime exists.

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

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Extensions

A088124 Let f(n,x) = 1 + 4x + 6x^2 + 8x^3 + 9x^4 + ... + composite(n)*x^n; a(n)= smallest prime f(n,x), or 0 if no such prime exists.

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Author

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cp's OEIS Frontend

A088123 Let f(n,x) = 1 + 2x + 3x^2 + 5x^3 + 7x^4 + ... + prime(n)*x^n; a(n) = smallest value of x such that f(n,x) is a prime, or 0 if no such prime exists.

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Author

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Examples

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Programs

Mathematica

Extensions

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.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Extensions

A088124 Let f(n,x) = 1 + 4x + 6x^2 + 8x^3 + 9x^4 + ... + composite(n)*x^n; a(n)= smallest prime f(n,x), or 0 if no such prime exists.

Views

Author

Keywords

Crossrefs

Extensions

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