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Search: id:A113777
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| A113777 |
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Minimal number m for which the sum of the k^n, k=1...m, is less than m!. |
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+0
1
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| 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85, 86, 87, 89, 90
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Minimal number m for which the sum of the k^n, k=1...m, is less than m!.
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FORMULA
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Let S(n, m)=sum[k^n | k=1...m}. Define a(n):= min{ m | S(n, m)<m! }
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EXAMPLE
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a(3)=6 because S(3,6)=441<720=6! but S(3,5)=225>=120=5! and so for S(3,j), j=0,1,2,3,4.
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CROSSREFS
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Sequence in context: A039179 A002328 A039133 this_sequence A039096 A083121 A026438
Adjacent sequences: A113774 A113775 A113776 this_sequence A113778 A113779 A113780
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 19 2006
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