A121926 a(n) = prime(n) + n!.

3, 5, 11, 31, 131, 733, 5057, 40339, 362903, 3628829, 39916831, 479001637, 6227020841, 87178291243, 1307674368047, 20922789888053, 355687428096059, 6402373705728061, 121645100408832067, 2432902008176640071, 51090942171709440073, 1124000727777607680079

Offset: 1

Author

N. J. A. Sloane, Aug 13 2008

Keywords

• nonn

Comments

It was conjectured by Alexander R. Povolotsky and proved (in SeqFan email exchange) by David L. Harden (with proof improvement from Daniel Berend) that no value of n exists such that ( n! + prime(n) ) yields an integral square. He also conjectured (see the link) that no value of n exists such that ( n! + prime(n) ) yields an integral m^k where k>1. - Alexander R. Povolotsky, Aug 13 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 1..445
• Carlos Rivera, Conjecture 59, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A063499.

Programs

Magma

[NthPrime(n) + Factorial(n): n in [1..30]]; // Vincenzo Librandi, Mar 22 2015

Mathematica

Table[Prime[n]+n!,{n,30}] (* Harvey P. Dale, Mar 23 2012 *)

PARI

a(n)=prime(n) + n! \\ Charles R Greathouse IV, Jan 27 2015

Formula

Sum_{n>=1} 1/a(n) = 0.6657239270705138461513344444... - Alexander R. Povolotsky, Sep 22 2008