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A371944
The binary expansion of a(n) corresponds to the ordinal transform (reduced modulo 2) of the binary expansion of n.
2
0, 1, 3, 2, 6, 6, 5, 5, 13, 12, 12, 13, 10, 11, 11, 10, 26, 26, 25, 25, 25, 25, 26, 26, 21, 21, 22, 22, 22, 22, 21, 21, 53, 52, 52, 53, 50, 51, 51, 50, 50, 51, 51, 50, 53, 52, 52, 53, 42, 43, 43, 42, 45, 44, 44, 45, 45, 44, 44, 45, 42, 43, 43, 42, 106, 106
OFFSET
0,3
COMMENTS
Leading zeros are ignored.
All terms belong to A063037.
FORMULA
A070939(a(n)) = A070939(n).
a(floor(n/2)) = floor(a(n)/2).
EXAMPLE
For n = 43: the binary expansion of 43 is "101011", the corresponding ordinal transform is "1, 1, 2, 2, 3, 4", reducing modulo 2 yields "110010", the binary expansion of a(43), so a(43) = 50.
MATHEMATICA
{0}~Join~Array[(c[0] = 1; c[1] = 1; FromDigits[Map[Mod[c[#]++, 2] &, IntegerDigits[#, 2] ], 2]) &, 120] (* Michael De Vlieger, Apr 16 2024 *)
PROG
(PARI) a(n) = { my (b = binary(n), f = vector(2)); for (i = 1, #b, b[i] = f[1+b[i]]++; ); fromdigits(b % 2, 2); }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 13 2024
STATUS
approved