A129977 - OEIS

%I #22 Oct 10 2022 07:56:55

%S 2,17,102,112,316,447,535,820,1396,1475,1650,5575,6486,6832

%N Numbers m such that A119029(m) = numerator(Sum_{k=1..m} m^(k-1)/k!) is prime.

%C For n >= 1, the corresponding primes are A119029(a(n)) = {2, 1676770323947695709, ...}.

%C a(15) > 10000. - _Lucas A. Brown_, Apr 01 2021

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A129977.py">A129977.py</a>

%t Do[ f=Numerator[ Sum[ n^(k-1)/k!, {k, 1, n} ] ]; If[ PrimeQ[f], Print[{n,f}] ], {n,1,316} ]

%t Select[Range[2000],PrimeQ[Numerator[Sum[#^(k-1)/k!,{k,#}]]]&] (* _Harvey P. Dale_, Jun 15 2019 *)

%o (PARI) for( n=1,1000, if( ispseudoprime( numerator( sum( k=1,n,n^(k-1)/k!))), print1(n", "))) \\ _M. F. Hasler_, Jun 18 2007

%Y Cf. A119029, A120266, A120267.

%K more,nonn

%O 1,1

%A _Alexander Adamchuk_, Jun 13 2007

%E Edited and extended (a(6)..a(8)) by _M. F. Hasler_, Jun 18 2007

%E More terms from _Ryan Propper_, Jan 12 2008

%E Various sections edited by _Petros Hadjicostas_, May 12 2020

%E a(12)-a(14) from _Lucas A. Brown_, Apr 01 2021