A274604 Running sum of Noergaard's "infinity sequence" A004718.

0, 1, 0, 2, 3, 3, 1, 4, 3, 5, 5, 6, 8, 7, 4, 8, 9, 9, 7, 10, 10, 11, 10, 12, 10, 13, 14, 14, 17, 15, 11, 16, 15, 17, 17, 18, 20, 19, 16, 20, 20, 21, 20, 22, 23, 23, 21, 24, 26, 25, 22, 26, 25, 27, 27, 28, 25, 29, 31, 30, 34, 31, 26, 32, 33, 33, 31, 34, 34, 35, 34, 36, 34, 37, 38, 38, 41, 39, 35, 40, 40, 41, 40, 42, 43, 43, 41, 44, 43, 45, 45, 46, 48

Offset

0,4

Comments

If s(n) is A004718, then a(2n) = n - s(n) and a(2n+1) = n+1.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Yu Hin (Gary) Au, Christopher Drexler-Lemire & Jeffrey Shallit, Notes and note pairs in Nørgård's infinity series, Journal of Mathematics and Music, Volume 11, 2017, Issue 1, pages 1-19.

Maple

b:= proc(n) option remember; local r; `if`(n=0, 0,
      `if`(irem(n, 2, 'r')=0, -b(r), b(r)+1))
    end:
a:= proc(n) a(n):= b(n)+`if`(n=0, 0, a(n-1)) end:
seq(a(n), n=0..100);  # Alois P. Heinz, Jun 30 2016

Mathematica

b[n_] := b[n] = Module[{q, r}, If[n == 0, 0, {q, r} = QuotientRemainder[n, 2]; If[r == 0, -b[q], b[q] + 1]]];
a[n_] := b[n] + If[n == 0, 0, a[n - 1]];
a /@ Range[0, 100] (* Jean-François Alcover, Nov 24 2020, after Alois P. Heinz *)

Prog

(Python)
from itertools import groupby
def A274604(n):
    if n&1: return (n>>1)+1
    c = 0
    for k, g in groupby(bin(m:=n>>1)[2:]):
        c = c+len(list(g)) if k == '1' else (-c if len(list(g))&1 else c)
    return m-c # Chai Wah Wu, Mar 03 2023

Crossrefs

Cf. A004718.

Sequence in context: A114104 A076780 A324733 * A089283 A288531 A323942

Adjacent sequences: A274601 A274602 A274603 * A274605 A274606 A274607

Keyword

nonn

Author

Jeffrey Shallit, Jun 30 2016

Status

approved