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A323355
a(1)=1; for n >= 2, a(n) = Sum_{i=1..A000120(n)} a(z(i)), where z(i) are the positions of 1's in the binary expansion of n, counted from left to right.
2
1, 1, 2, 1, 3, 2, 4, 1, 2, 3, 4, 2, 3, 4, 5, 1, 4, 2, 5, 3, 6, 4, 7, 2, 5, 3, 6, 4, 7, 5, 8, 1, 3, 4, 6, 2, 4, 5, 7, 3, 5, 6, 8, 4, 6, 7, 9, 2, 4, 5, 7, 3, 5, 6, 8, 4, 6, 7, 9, 5, 7, 8, 10, 1, 5, 3, 7, 4, 8, 6, 10, 2, 6, 4, 8, 5, 9, 7, 11, 3, 7, 5, 9, 6, 10, 8, 12, 4, 8, 6, 10, 7, 11, 9, 13, 2, 6, 4
OFFSET
1,3
LINKS
EXAMPLE
n=13, decimal 13 is 1101 in binary, the 1's are at positions 1,2,4. So a(13) = a(1) + a(2) + a(4).
MATHEMATICA
a[1] = 1; a[n_] := a[n] = Total[a /@ (Position[IntegerDigits[n, 2], 1] // Flatten)]; Array[a, 100] (* Amiram Eldar, Jul 24 2023 *)
PROG
(PARI) lista(nn) = {my(va = vector(nn), vb); va[1] = 1; for (n=2, nn, vb = binary(n); va[n] = sum(k=1, #vb, vb[k]*va[k]); ); va; } \\ Michel Marcus, Jan 12 2019
CROSSREFS
Sequence in context: A363489 A363944 A367581 * A367587 A363942 A363487
KEYWORD
base,nonn
AUTHOR
Ctibor O. Zizka, Jan 12 2019
STATUS
approved