A166266 Number of 1's in binary expansion of A000110(n).

1, 1, 1, 2, 4, 3, 5, 7, 4, 8, 8, 10, 10, 12, 14, 15, 15, 16, 22, 19, 25, 29, 25, 31, 25, 31, 28, 39, 32, 35, 41, 42, 46, 47, 46, 52, 49, 52, 59, 53, 59, 55, 75, 69, 58, 68, 62, 85, 81, 82, 55, 81, 82, 89, 89, 97, 87, 96, 92, 95, 103, 99, 120, 105, 105, 113, 106, 126, 125, 126

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1000 terms from Harvey P. Dale)

Javier Cilleruelo, Florian Luca, Juanjo Rué, and Ana Zumalacárregui, On the sum of digits of some sequences of integers, Open Mathematics, Vol. 11, No. 1 (2013), pp. 188-195.

Formula

a(n) = A000120(A000110(n)). - Alois P. Heinz, Jun 22 2022

a(n) > log_2(n)/60 on a set of positive integers n of asymptotic density 1 (Cilleruelo et al., 2013, Corollary 1.2, p. 191). - Amiram Eldar, Jan 11 2025

Maple

b:= proc(n) option remember; `if`(n=0, 1,
      add(b(n-j)*binomial(n-1, j-1), j=1..n))
    end:
a:= n-> add(i, i=Bits[Split](b(n))):
seq(a(n), n=0..80);  # Alois P. Heinz, Jun 22 2022

Mathematica

f[n_] := Plus @@ IntegerDigits[n, 2]; be[n_] := Sum[StirlingS2[n, k], {k, 0, n}]; lst = {}; Do[AppendTo[lst, f[be[n]]], {n, 0, 6!}]; lst
(* Second program: *)
DigitCount[#, 2, 1] & /@ BellB[Range[0, 70]] (* Harvey P. Dale, Dec 30 2018 *)

Prog

(Python)
from sympy import bell
def A166266(n): return int(bell(n)).bit_count() # Chai Wah Wu, Jun 22 2022
(Magma) [&+Intseq(Bell(n), 2): n in [0..100]]; // Vincenzo Librandi, Jan 05 2025

Crossrefs

Cf. A000110, A000120.

Sequence in context: A356385 A336640 A258238 * A011295 A377980 A082016

Adjacent sequences: A166263 A166264 A166265 * A166267 A166268 A166269

Keyword

nonn,base

Author

Vladimir Joseph Stephan Orlovsky, Oct 10 2009

Extensions

Edited by N. J. A. Sloane, Oct 13 2009

Offset corrected by Alois P. Heinz, Jun 22 2022

Status

approved