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A318571
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a(n) = ceiling(log(2)/(log(1+n/100))).
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0
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70, 36, 24, 18, 15, 12, 11, 10, 9, 8, 7, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1
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OFFSET
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1,1
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COMMENTS
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a(n) is the least positive integer k such that (1 + n/100)^k >= 2.
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LINKS
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Table of n, a(n) for n=1..100.
Wikipedia, Rule of 72
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FORMULA
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a(n) = 1 for n >= 100.
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EXAMPLE
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n | a(n) | Rule of 72 (= 72/n)
------+------+---------------------
1 | 70 | 72
2 | 36 | 36
3 | 24 | 24
4 | 18 | 18
5 | 15 | 14.4
6 | 12 | 12
7 | 11 | 10.285714...
8 | 10 | 9
9 | 9 | 8
10 | 8 | 7.2
11 | 7 | 6.545454...
12 | 7 | 6
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MAPLE
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seq(ceil(log(2)/(log(1+n/100))), n=1..100); # Muniru A Asiru, Aug 30 2018
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MATHEMATICA
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Table[Ceiling[Log[2]/Log[1 + n/100]], {n, 100}] (* Vincenzo Librandi, Sep 01 2018 *)
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PROG
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(PARI) {a(n) = ceil(log(2)/(log(1+n/100)))}
(Magma) [Ceiling(Log(2)/(Log(1+n/100))): n in [1..100]]; // Vincenzo Librandi, Sep 01 2018
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CROSSREFS
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Sequence in context: A361040 A033390 A129352 * A156810 A252714 A245046
Adjacent sequences: A318568 A318569 A318570 * A318572 A318573 A318574
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, Aug 29 2018
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STATUS
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approved
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