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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
OFFSET
0,4
COMMENTS
This sequence is a variant of A331362.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 17 2020
STATUS
approved