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A331362 a(n) is the greatest value of the form s_1 + ... + s_k such that the concatenation of the binary representations of s_1^2, ..., s_k^2 equals the binary representation of n. 4
0, 1, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 4, 4, 3, 3, 4, 3, 3, 3, 4, 3, 5, 3, 4, 4, 4, 4, 5, 4, 5, 3, 4, 6, 4, 4, 5, 3, 4, 3, 4, 4, 4, 4, 5, 5, 7, 5, 6, 4, 4, 4, 5, 4, 6, 4, 5, 5, 5, 5, 6, 8, 5, 5, 6, 4, 4, 4, 5, 6, 7, 4, 5, 5, 5, 5, 6, 5, 9, 4, 5, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

As 0 and 1 are squares, we can always split the binary representation of a number into squares, and the sequence is well defined.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Rémy Sigrist, Density plot of the first 2^20 terms

Rémy Sigrist, PARI program for A331362

Index entries for sequences related to binary expansion of n

FORMULA

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

a(n^2) = n.

EXAMPLE

For n = 8:

- the binary representation of 8 is "1000",

- we can split it into "100" and "0" (2^2 and 0^2),

- or into "1" and "0" and "0" and "0" (1^2 and 0^2 and 0^2 and 0^2),

- so a(8) = max(2+0, 1+0+0+0) = 2.

PROG

(PARI) See Links section.

CROSSREFS

Cf. A000120, A003754.

Sequence in context: A260235 A078120 A057525 * A139325 A216325 A322868

Adjacent sequences:  A331359 A331360 A331361 * A331363 A331364 A331365

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Jan 14 2020

STATUS

approved

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Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)