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A121926
a(n) = prime(n) + n!.
7
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
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 A372255
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 13 2008
STATUS
approved