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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 13 2008
STATUS
approved