

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.


1



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
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OFFSET

0,4


COMMENTS

This sequence is a variant of A331362.


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


FORMULA

a(n) >= A000120(n) with equality iff n belongs to A003754.
a(n^2) = n^2.


EXAMPLE

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.


PROG

(PARI) See Links section.


CROSSREFS

Cf. A000120, A003754, A331362.
Sequence in context: A218217 A218279 A183193 * A021809 A210210 A117007
Adjacent sequences: A331467 A331468 A331469 * A331471 A331472 A331473


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Jan 17 2020


STATUS

approved



