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

Author

Rémy Sigrist, Apr 04 2018

Keywords

• nonn
• base
• easy

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.

Examples

			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)
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A059711, A302291.

Programs

PARI

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

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).