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%I #43 Sep 08 2022 08:45:27
%S 3,5,11,31,131,733,5057,40339,362903,3628829,39916831,479001637,
%T 6227020841,87178291243,1307674368047,20922789888053,355687428096059,
%U 6402373705728061,121645100408832067,2432902008176640071,51090942171709440073,1124000727777607680079
%N a(n) = prime(n) + n!.
%C 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
%H G. C. Greubel, <a href="/A121926/b121926.txt">Table of n, a(n) for n = 1..445</a>
%H Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_059.htm">Conjecture 59</a>, The Prime Puzzles and Problems Connection.
%F Sum_{n>=1} 1/a(n) = 0.6657239270705138461513344444... - _Alexander R. Povolotsky_, Sep 22 2008
%t Table[Prime[n]+n!,{n,30}] (* _Harvey P. Dale_, Mar 23 2012 *)
%o (PARI) a(n)=prime(n) + n! \\ _Charles R Greathouse IV_, Jan 27 2015
%o (Magma) [NthPrime(n) + Factorial(n): n in [1..30]]; // _Vincenzo Librandi_, Mar 22 2015
%Y Cf. A063499.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Aug 13 2008
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