A337224 a(n) is the least number that can be obtained by replacing some repetitive part X^k in the binary expansion of n by X.

0, 1, 2, 1, 2, 5, 2, 1, 2, 5, 2, 5, 4, 5, 2, 1, 2, 5, 10, 9, 4, 5, 10, 5, 6, 9, 6, 11, 4, 5, 2, 1, 2, 5, 10, 11, 4, 9, 18, 9, 8, 9, 2, 11, 20, 5, 10, 5, 6, 13, 18, 19, 12, 13, 6, 13, 8, 9, 10, 11, 4, 5, 2, 1, 2, 5, 10, 11, 20, 17, 22, 17, 8, 9, 18, 19, 36, 37

Offset: 0

Author

Rémy Sigrist, Aug 19 2020

Keywords

• nonn
• base

Comments

Leading zeros in binary expansions are ignored.

There are four fixed points: 0, 1, 2 and 5; their binary expansion is a squarefree string.

Examples

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2      10         10
   3     1      11          1
   4     2     100         10
   5     5     101        101
   6     2     110         10
   7     1     111          1
   8     2    1000         10
   9     5    1001        101
  10     2    1010         10
  11     5    1011        101
  12     4    1100        100
  13     5    1101        101
  14     2    1110         10
  15     1    1111          1
  16     2   10000         10
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, PARI program for A337224
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A337222, A337223.

Programs

PARI

See Links section.

Formula

a(n) = 1 iff n = 2^k-1 for some k > 0.