A124375 Numbers k such that A003422(k+1)/2 is prime.

2, 3, 4, 7, 8, 9, 10, 29, 75, 162, 270, 272, 353, 720, 1795, 3732, 4768, 9315, 12220, 41531

Offset

1,1

Comments

Sum_{i=0..k} i! = k! + !k = A003422(k+1), where !k is left factorial !k = Sum_{i=0..k-1} i! = A003422(k). Left factorials are even for k > 1. Corresponding primes of the form (k! + !k)/2 = (a(n)! + !a(n))/2 are listed in A124374(n) = {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..20.

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}]
Flatten[Position[Accumulate[(Range[0, 12220]!)]/2, _?PrimeQ]]-1 (* Harvey P. Dale, Jul 02 2019 *)

Crossrefs

Cf. A003422, A124374.

Sequence in context: A152979 A070942 A073798 * A287664 A037080 A167055

Adjacent sequences: A124372 A124373 A124374 * A124376 A124377 A124378

Keyword

nonn,more,hard

Author

Alexander Adamchuk, Oct 28 2006

Extensions

More terms from Ryan Propper, Feb 07 2008

a(20) from Jinyuan Wang, Mar 20 2021

Status

approved