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A371974
For any positive integer n with binary expansion (b_1, ..., b_w) (where b_1 = 1), the binary expansion of a(n) is (c_1, ..., c_w) with c_k = (Sum_{i = 1 mod (w+1-k)} b_i) mod 2 for k = 1..w; a(0) = 0.
3
0, 1, 3, 2, 7, 4, 6, 5, 15, 10, 12, 9, 14, 11, 13, 8, 31, 20, 26, 17, 28, 23, 25, 18, 30, 21, 27, 16, 29, 22, 24, 19, 63, 46, 52, 37, 58, 43, 49, 32, 60, 45, 55, 38, 57, 40, 50, 35, 62, 47, 53, 36, 59, 42, 48, 33, 61, 44, 54, 39, 56, 41, 51, 34, 127, 88, 110
OFFSET
0,3
COMMENTS
This sequence is a permutation of the nonnegative integers with inverse A371975.
FORMULA
A070939(a(n)) = A070939(n).
a(n) mod 2 = A010060(n).
EXAMPLE
For n = 42: the binary expansion of 42 is "101010":
b_1 b_2 b_3 b_4 b_5 b_6
1 0 1 0 1 0
c_1 = 1 = 1 mod 2
c_2 = 1 + 0 = 1 mod 2
c_3 = 1 + 1 = 0 mod 2
c_4 = 1 + 0 = 1 mod 2
c_5 = 1 + 1 + 1 = 1 mod 2
c_6 = 1 + 0 + 1 + 0 + 1 + 0 = 1 mod 2
- so the binary expansion of a(42) is "110111", and a(42) = 55.
PROG
(PARI) a(n) = { my (b = binary(n), c = vector(#b)); for (k = 1, #c, forstep (i = 1, #b, #b+1-k, c[k] += b[i]; ); ); fromdigits(c % 2, 2); }
CROSSREFS
See A341335 and A371976 for similar sequences.
Cf. A010060, A070939, A371975 (inverse).
Sequence in context: A341911 A341916 A360960 * A344878 A344875 A178910
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 14 2024
STATUS
approved