A136273 a(0) = 0; for n>0, a(n) = period length of the decimal expansion of the number Sum_{i>=1} 2^(-n*i). Also period length of the fractions 1/b(n), where b(n) = 2*b(n-1) + 1, with b(1)=1.

0, 1, 6, 1, 15, 6, 42, 16, 24, 30, 44, 6, 1365, 42, 150, 256, 3855, 72, 74898, 30, 336, 1364, 44620, 240, 900, 2730, 262656, 336, 39672, 1650, 195225786, 65536, 1198956, 131070, 92190, 216, 616318176, 524286, 2123940, 61680, 26815350376, 43344

Offset

0,3

Comments

In base 2 consider the numbers 0.1111111..., 0.01010101...., 0.001001001..., 0.000100010001.... where the period [0 k times, 1], where k=0,1,2,3,.... Then convert to base 10. The sequence gives the length of each period.

The period length of the fraction 1/A000225(n) = 1/(2^n-1) for n>0. - Robert G. Wilson v, Mar 30 2008

Links

Table of n, a(n) for n=0..41.

Mathematica

f[n_] := Length[RealDigits[Sum[2^(-n*k), {k, Infinity}]][[1, 1]]]; Array[f, 36] (* Robert G. Wilson v, Mar 30 2008 *)

Crossrefs

Sequence in context: A147483 A050309 A103217 * A125233 A139727 A257468

Adjacent sequences: A136270 A136271 A136272 * A136274 A136275 A136276

Keyword

easy,nonn,base

Author

Paolo P. Lava & Giorgio Balzarotti, Mar 19 2008

Extensions

More terms from Robert G. Wilson v, Mar 30 2008

Status

approved