A387409 Partial sums of A387422 minus partial sums of A387412.

0, 0, 0, -2, -2, -1, -1, -1, -1, -3, -3, -2, -1, 0, 1, 0, 0, -1, -1, 2, 3, 3, 3, 4, 2, 0, -1, 2, 2, 1, 1, 1, -3, -3, -5, -4, -2, -4, -5, -5, -5, -8, -8, -6, -7, -8, -8, -10, -10, -10, -10, -8, -6, -5, -5, -3, -8, -8, -8, -8, -5, -5, -4, -5, -4, -2, -2, -3, -5, -3, -3, -4, -3, -3, -3, -1, -3, -2, -2, -1, -2, -3, -2

Offset

1,4

Comments

Also partial sums of A387413 minus partial sums of A387423.

This sequence gives some measure of how much longer the common prefix of the binary expansions of n and sigma(n) is - on average - than the common prefix of the binary expansions of n and A003961(n).

Question: Does the sequence eventually grow without limit and is it just because A003961(n) >= A000203(n)? Does ratio a(n)/n converge to any limit?

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

A. Karttunen, Ratio a(n)/n, plotted with OEIS Plot2-tool

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

Formula

a(n) = A387407(n) - A387408(n).

a(n) = A387425(n) - A387424(n).

Prog

(PARI) A387409(n) = (A387407(n) - A387408(n));

Crossrefs

Cf. A000203, A003961, A387407, A387408, A387412, A387413, A387422, A387423, A387424, A387425.

Sequence in context: A211999 A175025 A076899 * A152905 A096601 A078077

Adjacent sequences: A387406 A387407 A387408 * A387410 A387411 A387412

Keyword

sign,base

Author

Antti Karttunen, Sep 03 2025

Status

approved