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 A124374 Primes of the form (n! + !n)/2 = !(n + 1)/2 = Sum[ k!, {k,0,n} ]/2. 1
 2, 5, 17, 2957, 23117, 204557, 2018957, 4578979328975537786697650470157, 12572230784049013026617689884981971446439568309146114097251787122217783800812199225999909965168264460210470157 (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 numbers n such that Sum[ k!, {k,0,n} ]/2 = A003422(n+1)/2 is prime are listed in A124375(n) = {2,3,4,7,8,9,10,29,75,162,270,272,353,...}. LINKS Hisanori Mishima, Factorizations of many number sequences. Eric Weisstein's World of Mathematics, Left Factorial. FORMULA a(n) = A003422[ A124375(n) + 1 ]/2. MATHEMATICA f=0; Do[f=f+n!; If[PrimeQ[f/2], Print[{n, f/2}]], {n, 0, 353}] CROSSREFS Cf. A003422, A124375. Sequence in context: A128000 A281312 A182313 * A113617 A226069 A258429 Adjacent sequences:  A124371 A124372 A124373 * A124375 A124376 A124377 KEYWORD nonn AUTHOR Alexander Adamchuk, Oct 28 2006 STATUS approved

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Last modified April 5 10:33 EDT 2020. Contains 333239 sequences. (Running on oeis4.)