

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
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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



