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Search: id:A124375
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| A124375 |
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Numbers n such that Sum[ k!, {k,0,n} ]/2 = A003422(n+1)/2 is prime. |
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3
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| 2, 3, 4, 7, 8, 9, 10, 29, 75, 162, 270, 272, 353, 720, 1795, 3732, 4768, 9315, 12220
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (rpropper(AT)cs.stanford.edu), Feb 07 2008
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LINKS
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Hisanori Mishima, Factorizations of many number sequences.
Eric Weisstein's World of Mathematics, Left Factorial.
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MATHEMATICA
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f=0; Do[f=f+n!; If[PrimeQ[f/2], Print[{n, f/2}]], {n, 0, 353}]
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CROSSREFS
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Cf. A003422, A124374.
Adjacent sequences: A124372 A124373 A124374 this_sequence A124376 A124377 A124378
Sequence in context: A112965 A070942 A073798 this_sequence A037080 A022162 A022164
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KEYWORD
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hard,more,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 28 2006
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EXTENSIONS
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More terms from Ryan Propper (rpropper(AT)cs.stanford.edu), Feb 07 2008
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