

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.


1



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



FORMULA

a(2^k1) = k^2 for any k >= 0.
a(2^k) = k^2+1 for any k >= 0.


EXAMPLE

For n = 49:
 the binary representation of 49 is "110001",
 we have a run of 2 1's followed by a run of 3 0's followed by a run of 1 1's,
 so a(49) = 2^2 + 3^2 + 1^2 = 14.


PROG

(PARI) a(n) = { my (v=0); while (n, my (r=valuation(n+(n%2), 2)); v+=r^2; n\=2^r); v }


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



