A302295 a(n) is the period of the binary expansion of n (with leading zeros allowed).

1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 2, 4, 4, 4, 4, 1, 5, 4, 3, 5, 5, 2, 5, 5, 5, 5, 5, 3, 5, 5, 5, 1, 6, 5, 4, 6, 3, 6, 6, 6, 6, 6, 2, 6, 6, 3, 6, 6, 6, 6, 6, 4, 6, 6, 3, 6, 6, 6, 6, 6, 6, 6, 6, 1, 7, 6, 5, 7, 4, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 7

Offset

0,3

Comments

Equivalently, a(n) is the least positive k such that n is a repdigit number in base 2^k.

See A302291 for the variant where leading zeros are not allowed.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Index entries for sequences related to binary expansion of n

Formula

a(2^n) = n + 1 for any n >= 0.

a(2^n - 1) = 1 for any n >= 0.

a(n) <= A302291(n).

A059711(n) <= 2^a(n).

Example

The first terms, alongside the binary expansion of n with periodic part in parentheses, are:
  n  a(n)    bin(n)
  -- ----    ------
   0    1    (0)
   1    1    (1)
   2    2    (10)
   3    1    (1)(1)
   4    3    (100)
   5    2    (01)(01)
   6    3    (110)
   7    1    (1)(1)(1)
   8    4    (1000)
   9    3    (001)(001)
  10    2    (10)(10)
  11    4    (1011)
  12    4    (1100)
  13    4    (1101)
  14    4    (1110)
  15    1    (1)(1)(1)(1)
  16    5    (10000)
  17    4    (0001)(0001)
  18    3    (10)(10)
  19    5    (10011)
  20    5    (10100)

Prog

(PARI) a(n) = for (k=1, oo, if (#Set(digits(n, 2^k))<=1, return (k)))

Crossrefs

Cf. A059711, A302291.

Sequence in context: A097285 A057432 A361942 * A215467 A284266 A317988

Adjacent sequences: A302292 A302293 A302294 * A302296 A302297 A302298

Keyword

nonn,base,easy

Author

Rémy Sigrist, Apr 04 2018

Status

approved