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A381934 a(n) is the least k > 1 such that the binary expansions of n and n*k have the same number of nonleading zeros.

%I A381934 #17 Mar 30 2025 20:27:37
%S A381934 2,3,3,5,3,6,5,9,3,5,6,5,5,19,9,17,3,5,5,3,6,9,5,11,5,7,19,301,9,35,
%T A381934 17,33,3,5,5,3,5,5,3,3,6,5,9,5,5,17,11,305,5,7,7,15,19,3,301,9,9,71,
%U A381934 35,13,17,67,33,65,3,5,5,3,5,5,3,3,5,10,5,10,3,6
%N A381934 a(n) is the least k > 1 such that the binary expansions of n and n*k have the same number of nonleading zeros.
%C A381934 This sequence is well defined (see A381935).
%H A381934 Rémy Sigrist, <a href="/A381934/b381934.txt">Table of n, a(n) for n = 0..8192</a>
%H A381934 Rémy Sigrist, <a href="/A381934/a381934.gp.txt">PARI program</a>
%F A381934 a(2^n) = 3.
%F A381934 a(2^n - 1) = 2^n + 1.
%e A381934 The first terms, alongside the binary expansions of n and n*a(n), are:
%e A381934   n   a(n)  bin(n)  bin(n*a(n))
%e A381934   --  ----  ------  -----------
%e A381934    0     2       0            0
%e A381934    1     3       1           11
%e A381934    2     3      10          110
%e A381934    3     5      11         1111
%e A381934    4     3     100         1100
%e A381934    5     6     101        11110
%e A381934    6     5     110        11110
%e A381934    7     9     111       111111
%e A381934    8     3    1000        11000
%e A381934    9     5    1001       101101
%e A381934   10     6    1010       111100
%e A381934   11     5    1011       110111
%e A381934   12     5    1100       111100
%e A381934   13    19    1101     11110111
%e A381934   14     9    1110      1111110
%e A381934   15    17    1111     11111111
%e A381934   16     3   10000       110000
%o A381934 (PARI) \\ See Links section.
%Y A381934 Cf. A023416, A292849, A295827, A352217, A381935.
%K A381934 nonn,base
%O A381934 0,1
%A A381934 _Rémy Sigrist_, Mar 10 2025