A356354 a(n) is the least k such that the sets of positions of 1's in the binary expansions of n and k are similar.

0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 11, 3, 11, 7, 15, 1, 3, 3, 19, 3, 7, 11, 23, 3, 19, 11, 27, 7, 23, 15, 31, 1, 3, 3, 35, 3, 37, 19, 39, 3, 37, 7, 43, 11, 45, 23, 47, 3, 35, 19, 51, 11, 43, 27, 55, 7, 39, 23, 55, 15, 47, 31, 63, 1, 3, 3, 67, 3, 11, 35, 71, 3, 7

Offset

0,4

Comments

Let s(n) be the set of terms in the n-th row of A133457 (with s(0) = {}).

a(n) is the least k such that s(n) is the image of s(k) under some nonconstant linear function.

Links

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

Rémy Sigrist, PARI program

Wikipedia, Similarity (geometry)

Index entries for sequences related to binary expansion of n

Formula

A000120(a(n)) = A000120(n).

a(a(n)) = a(n).

a(2*n) = a(n).

a(A030101(n)) = a(n).

a(n) = 1 iff n is a power of 2.

a(n) = 3 iff n belongs to A018900.

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A000120, A000265, A018900, A030101, A064895, A133457.

Sequence in context: A246591 A173465 A151837 * A355339 A331856 A163381

Adjacent sequences: A356351 A356352 A356353 * A356355 A356356 A356357

Keyword

nonn,base

Author

Rémy Sigrist, Oct 15 2022

Status

approved