A126726 Number of squares (of nonnegative integers) that require n binary (base-2) digits.

0, 2, 0, 1, 1, 2, 2, 4, 4, 7, 9, 14, 18, 27, 37, 54, 74, 107, 149, 213, 299, 425, 599, 849, 1199, 1697, 2399, 3394, 4798, 6787, 9597, 13573, 19195, 27146, 38390, 54292, 76780, 108584, 153560, 217168, 307120, 434335, 614241, 868669, 1228483, 1737338, 2456966

Offset: 0

Author

Andrew G. West (westa(AT)wlu.edu), Mar 13 2007

Keywords

• base
• easy
• nonn

Comments

Binary equivalent to A062940, which uses decimal representation.

Examples

			21^2 = 441 = 110111001_2, requiring 9 digits.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A062940.

Programs

Maple

r:= proc(n) local b; b:= isqrt(n); b+`if`(b^2 `if`(n=0, 0, r(2^n) -r(2^(n-1)) +`if`(n=1, 1, 0)):
seq(a(n), n=0..50);  # Alois P. Heinz, Sep 13 2012

Formula

Conjecture: a(n) = A190568(n)-(-1)^n for n>0. - R. J. Mathar, May 21 2025