A318571 a(n) = ceiling(log(2)/(log(1+n/100))).

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

Offset

1,1

Comments

a(n) is the least positive integer k such that (1 + n/100)^k >= 2.

Links

Table of n, a(n) for n=1..100.

Wikipedia, Rule of 72

Formula

a(n) = 1 for n >= 100.

Example

   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

Maple

seq(ceil(log(2)/(log(1+n/100))), n=1..100); # Muniru A Asiru, Aug 30 2018

Mathematica

Table[Ceiling[Log[2]/Log[1 + n/100]], {n, 100}] (* Vincenzo Librandi, Sep 01 2018 *)

Prog

(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

Crossrefs

Sequence in context: A361040 A033390 A129352 * A156810 A252714 A245046

Adjacent sequences: A318568 A318569 A318570 * A318572 A318573 A318574

Keyword

nonn

Author

Seiichi Manyama, Aug 29 2018

Status

approved