A175406 The greatest integer k such that (1+1/n)^k <= 2.

1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 44, 44, 45, 46, 46, 47, 48, 48, 49, 50, 50, 51

Offset

1,3

Comments

The sequence of first differences consists of zeros and ones, with no two consecutive zeros and no more than three consecutive ones.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = n log 2 + O(1). Conjecture: a(n) = floor((n + 1/2) log 2). - Charles R Greathouse IV, Apr 03 2012

Maple

f:= n -> floor(ln(2)/ln(1+1/n)):
map(f, [$1..100]); # Robert Israel, Mar 09 2026

Mathematica

Table[Floor[Log[(1+1/n), 2]], {n, 200}]

Prog

(PARI) a(n)=log(2)\log(1+1/n) \\ Charles R Greathouse IV, Apr 03 2012

Crossrefs

Cf. A094500.

Sequence in context: A066481 A248103 A121928 * A210435 A181534 A258703

Adjacent sequences: A175403 A175404 A175405 * A175407 A175408 A175409

Keyword

nonn

Author

Zak Seidov, May 01 2010

Extensions

Name corrected (to match terms) by Jon E. Schoenfield, Apr 23 2014

Status

approved