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A186109
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Numerator of the cumulative frequency of the dropping time in the Collatz iteration.
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3
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1, 3, 13, 7, 115, 237, 15, 1935, 7825, 31473, 31711, 254649, 15957, 2050541, 8219801, 16490635, 33035745, 132455435, 530485275, 1061920785, 4253619813, 4256987887, 34095896991, 136471574881, 273072139013, 136638599097, 2187167322891, 4377196161075, 4378797345767, 35049397190341
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OFFSET
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1,2
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COMMENTS
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The possible dropping times are in A020914. The denominators are in A186110. The frequency of the n-th dropping time is A186107(n)/A186108(n).
Riho Terras' classic paper about the Collatz problem shows the decimal values of 2(1-c(k)) in Table A, where c(k) is the cumulative frequency of dropping times <= k.
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LINKS
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FORMULA
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EXAMPLE
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The cumulative frequencies are 1/2, 3/4, 13/16, 7/8, 115/128, 237/256, 15/16, 1935/2048, 7825/8192, ... .
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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