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A124375 Numbers n such that Sum[ k!, {k,0,n} ]/2 = A003422(n+1)/2 is prime. 2
2, 3, 4, 7, 8, 9, 10, 29, 75, 162, 270, 272, 353, 720, 1795, 3732, 4768, 9315, 12220 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sum[ k!, {k,0,n} ] = n! + !n = !(n+1) = A003422(n+1), where !n is left factorial !n = Sum[ k!, {k,0,n-1} ] = A003422(n) = {0, 1, 2, 4, 10, 34, 154, 874, 5914, 46234, 409114, 4037914, ...}. Left factorials are even for n>1. Corresponding primes of the form (k!+!k)/2 = (a(n)!+!a(n))/2 are listed in A124374(n) = A003422[a(n)+1]/2 = {2, 5, 17, 2957, 23117, 204557, 2018957, 4578979328975537786697650470157,...}.

A near-duplicate of A100614: a(n) = A100614(n) - 1. - Ryan Propper, Feb 07 2008

LINKS

Table of n, a(n) for n=1..19.

Hisanori Mishima, Factorizations of many number sequences.

Eric Weisstein's World of Mathematics, Left Factorial.

MATHEMATICA

f=0; Do[f=f+n!; If[PrimeQ[f/2], Print[{n, f/2}]], {n, 0, 353}]

CROSSREFS

Cf. A003422, A124374.

Sequence in context: A152979 A070942 A073798 * A287664 A037080 A167055

Adjacent sequences:  A124372 A124373 A124374 * A124376 A124377 A124378

KEYWORD

hard,more,nonn

AUTHOR

Alexander Adamchuk, Oct 28 2006

EXTENSIONS

More terms from Ryan Propper, Feb 07 2008

STATUS

approved

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Last modified June 17 14:09 EDT 2019. Contains 324185 sequences. (Running on oeis4.)