A331470 a(n) is the greatest value of the form s_1^2 + ... + s_k^2 such that the concatenation of the binary representations of s_1^2, ..., s_k^2 equals the binary representation of n.

0, 1, 1, 2, 4, 2, 2, 3, 4, 9, 2, 3, 5, 3, 3, 4, 16, 5, 9, 10, 5, 3, 3, 4, 5, 25, 3, 4, 6, 4, 4, 5, 16, 17, 5, 6, 36, 10, 10, 11, 5, 10, 3, 4, 6, 4, 4, 5, 17, 49, 25, 26, 6, 4, 4, 5, 6, 26, 4, 5, 7, 5, 5, 6, 64, 17, 17, 18, 8, 6, 6, 7, 36, 37, 10, 11, 13, 11

Offset: 0

Author

Rémy Sigrist, Jan 17 2020

Keywords

• nonn
• base

Comments

This sequence is a variant of A331362.

Examples

			For n = 12:
- the binary representation of 12 is "1100",
- we can split it into "1" and "1" and "0" and "0" (1^2 and 1^2 and 0^2 and 0^2),
- or into "1" and "100" (1^2 and 2^2),
- hence a(12) = max(2, 5) = 5.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Rémy Sigrist, PARI program for A331470
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A003754, A331362.

Programs

PARI

See Links section.

Formula

a(n) >= A000120(n) with equality iff n belongs to A003754.

a(n^2) = n^2.