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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified February 5 15:15 EST 2023. Contains 360086 sequences. (Running on oeis4.)