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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.
1
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 15 2022
STATUS
approved