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%I #32 May 05 2021 13:50:04
%S 5,10,9,20,21,18,17,40,19,42,38,36,37,34,33,80,35,38,37,84,35,76,74,
%T 72,73,74,70,68,69,66,65,160,67,70,69,76,67,74,73,168,75,70,69,152,67,
%U 148,146,144,71,146,145,148,140,140,138,136,137,138,134,132,133
%N a(n) is the least k > 0 such that the binary expansions of k and of n + k have the same numbers of 0's and of 1's.
%C This is the binary analog of A343888.
%H Rémy Sigrist, <a href="/A343852/b343852.txt">Table of n, a(n) for n = 1..8191</a>
%F a(n) <= A004757(n).
%e The first terms, alongside the binary expansions of a(n) and of n + a(n), are:
%e n a(n) bin(a(n)) bin(n+a(n))
%e -- ---- --------- -----------
%e 1 5 101 110
%e 2 10 1010 1100
%e 3 9 1001 1100
%e 4 20 10100 11000
%e 5 21 10101 11010
%e 6 18 10010 11000
%e 7 17 10001 11000
%e 8 40 101000 110000
%e 9 19 10011 11100
%e 10 42 101010 110100
%e 11 38 100110 110001
%e 12 36 100100 110000
%e 13 37 100101 110010
%e 14 34 100010 110000
%e 15 33 100001 110000
%o (PARI) a(n) = { for (k=1, oo, if (#binary(k)==#binary(n+k) && hammingweight(k)==hammingweight(n+k), return (k))) }
%o (Python)
%o def a(n):
%o k = 1
%o while k.bit_length() != (n+k).bit_length() or bin(k).count('1') != bin(n+k).count('1'): k += 1
%o return k
%o print([a(n) for n in range(1, 62)]) # _Michael S. Branicky_, May 04 2021
%Y Cf. A000120, A004757, A023416, A293198, A343888.
%K nonn,base
%O 1,1
%A _Rémy Sigrist_, May 03 2021
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