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Search: id:A122990
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| A122990 |
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Numbers n such that Sum[ k!, {k,1,n} ]/99 = A007489(n)/99 is prime. |
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+0
2
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| 8, 10, 11, 16, 22, 30, 34, 40, 42, 47, 49, 68, 74, 79, 168, 202, 245, 280, 463, 534
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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A007489(n) = Sum[ k!, {k,1,n} ] = (!(n+1) - 1) = A003422(n+1) - 1 = {0, 1, 3, 9, 33, 153, 873, 5913, 46233, 409113, 4037913, ...}. A007489(n) is divisible by 99 for n=8 and n>9. Corresponding primes of the form (!(n+1) - 1)/99 are {467, 40787, 443987, 225498914387, 11895484822660898387, 2771826449193354891007108898387, 3072603482270933019578343003268898387, ...}.
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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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PROGRAM
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(ARIBAS) f=0; Do[f=f+n!; If[PrimeQ[f/99], Print[{n, f/99}]], {n, 1, 534}]
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CROSSREFS
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Cf. A007489, A003422 - Left factorial.
Sequence in context: A031037 A006757 A126803 this_sequence A062372 A046031 A102758
Adjacent sequences: A122987 A122988 A122989 this_sequence A122991 A122992 A122993
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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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