A332017 - OEIS

A332017

a(n) is the sum of the squares of the lengths of the runs of consecutive equal digits in the binary representation of n.

0, 1, 2, 4, 5, 3, 5, 9, 10, 6, 4, 6, 8, 6, 10, 16, 17, 11, 7, 9, 7, 5, 7, 11, 13, 9, 7, 9, 13, 11, 17, 25, 26, 18, 12, 14, 10, 8, 10, 14, 12, 8, 6, 8, 10, 8, 12, 18, 20, 14, 10, 12, 10, 8, 10, 14, 18, 14, 12, 14, 20, 18, 26, 36, 37, 27, 19, 21, 15, 13, 15, 19

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OFFSET

0,3

COMMENTS

a(0) = 0 by convention.

Every nonnegative number k appears A006456(k) times in the sequence, the last occurrence being at index A000975(k).

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = Sum_{k = 1..A005811(n)} A101211(n, k)^2.

a(A000975(k)) = k for any k >= 0.