A337222 a(n) is the least number that can be obtained by replacing some square XX in the binary expansion of n by X.

0, 1, 2, 1, 2, 5, 2, 3, 4, 5, 2, 5, 4, 5, 6, 3, 4, 9, 10, 9, 4, 5, 10, 11, 8, 9, 6, 11, 12, 13, 6, 7, 8, 9, 18, 17, 4, 9, 18, 19, 8, 9, 10, 11, 20, 5, 22, 11, 12, 17, 18, 19, 12, 13, 6, 23, 24, 25, 14, 27, 12, 13, 14, 7, 8, 17, 18, 19, 34, 17, 34, 35, 8, 9, 18

Offset

0,3

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Rémy Sigrist, PARI program for A337222

Index entries for sequences related to binary expansion of n

Formula

a(A020330(n)) = n for any n > 0.

Example

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     3     111         11
   8     4    1000        100
   9     5    1001        101
  10     2    1010         10
  11     5    1011        101
  12     4    1100        100
  13     5    1101        101
  14     6    1110        110
  15     3    1111         11
  16     4   10000        100

Prog

(PARI) See Links section.

Crossrefs

Cf. A020330, A337223, A337224.

Sequence in context: A144155 A109631 A361399 * A095149 A218579 A329198

Adjacent sequences: A337219 A337220 A337221 * A337223 A337224 A337225

Keyword

nonn,base

Author

Rémy Sigrist, Aug 19 2020

Status

approved