A324608 Number of 1's in binary expansion of A308092(n).

1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 10, 11, 11, 11, 13, 13, 14, 14, 14, 16, 16, 16, 17, 17, 17, 19, 19, 19, 19, 20, 20, 20, 22, 22, 22, 22, 22, 23, 23, 23, 25, 25, 25, 25, 25, 25, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 29, 29, 30, 31, 31, 31, 31, 31, 31, 31, 31

Offset

1,3

Comments

Conjecture: sequence is weakly increasing.

Links

Robert Israel, Table of n, a(n) for n = 1..3000

Formula

a(n) = A000120(A308092(n)).

Maple

S:= "110":
b("0"):= 0: b("1"):= 1:
A308092[1]:= 1: A308092[2]:= 2: t:= 3:
for n from 3 to 300 do
  tp:= add(b(S[i])*2^(n-i), i=1..n);
  A308092[n]:= tp - t;
  t:= tp;
  S:= cat(S, convert(A308092[n], binary));
od:
seq(convert(convert(A308092[n], base, 2), `+`), n=1..300); # Robert Israel, Jun 12 2019

Mathematica

a[1]=1; a[2]=2; a[n_]:=a[n]=FromDigits[Flatten[IntegerDigits[#, 2]&/@Table[a[k], {k, n-1}]][[;; n]], 2]-Total@Table[a[m], {m, n-1}]
Count[#, 1]&/@Table[IntegerDigits[a[l], 2], {l, 70}] (* Giorgos Kalogeropoulos, Mar 30 2021 *)

Prog

(Python)
def aupton(terms):
  alst, bstr = [1, 1], "110"
  for n in range(3, terms+1):
    an = int(bstr[:n], 2) - int(bstr[:n-1], 2)
    binan = bin(an)[2:]
    alst, bstr = alst + [binan.count('1')], bstr + binan
  return alst
print(aupton(68)) # Michael S. Branicky, Mar 30 2021

Crossrefs

Cf. A000120, A308092.

Sequence in context: A102680 A025791 A358474 * A237115 A362915 A069637

Adjacent sequences: A324605 A324606 A324607 * A324609 A324610 A324611

Keyword

nonn,base

Author

Peter Kagey, Jun 10 2019

Status

approved