A216685 a(n) is the number of 1's in binary expansion of n + a(n-1), with a(0)=0.

0, 1, 2, 2, 2, 3, 2, 2, 2, 3, 3, 3, 4, 2, 1, 1, 2, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 5, 2, 5, 3, 2, 2, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 5, 3, 2, 2, 3, 4, 4, 4, 5, 4, 4, 4, 5, 5, 5, 6, 2, 5, 2, 1, 1, 2, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 5, 3, 2, 2, 3, 4, 4, 4, 5, 4, 4, 4

Offset

0,3

Comments

Indices of 1's: 1, 14, 15, 62, 63, 254, 255, 2045, 4087, 32766, 32767, 65523, 131069, 262129, 524272, 524286, 524287, 2097149, 8388605, 16777195, 16777212, ...

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(0) = 0, a(n) = A000120(n+a(n-1)).

Mathematica

a[0] = 0; a[n_] := a[n] = DigitCount[n + a[n - 1], 2, 1]; Array[a, 100, 0] (* Amiram Eldar, Jul 22 2023 *)

Prog

(Python)
a=0
for n in range(1, 333):
    print(a, end=', ')
    x = a+n
    a = 0
    while x:
        a += x & 1
        x >>= 1

Crossrefs

Cf. A000120.

Sequence in context: A127656 A109709 A125604 * A331853 A187184 A301375

Adjacent sequences: A216682 A216683 A216684 * A216686 A216687 A216688

Keyword

nonn,base

Author

Alex Ratushnyak, Sep 14 2012

Status

approved