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

1,1

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.

Formula

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

Mathematica

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

Prog

(PARI) a(n)=prime(n) + n! \\ Charles R Greathouse IV, Jan 27 2015
(Magma) [NthPrime(n) + Factorial(n): n in [1..30]]; // Vincenzo Librandi, Mar 22 2015

Crossrefs

Cf. A063499.

Sequence in context: A095184 A048235 A154939 * A063499 A285381 A082856

Adjacent sequences: A121923 A121924 A121925 * A121927 A121928 A121929

Keyword

nonn

Author

N. J. A. Sloane, Aug 13 2008

Status

approved