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A357656
a(n) is a lower bound for the largest Hamming weight of squares with exactly n binary zeros.
1
1, 0, 13, 8, 13, 16, 37, 38, 44
OFFSET
0,3
COMMENTS
The terms from a(2) onwards must be regarded as lower bounds, because no proof for the non-existence of squares with a very small number of binary zeros in the range k^2 > 2^90 (see b-file of A230097) is known.
a(9) >= 63, a(10) >= 57.
EXAMPLE
n a(n) bits k k^2 k^2 in binary
0 1 1 1 1 1
1 0 1 0 0 0
2 13 15 181 32761 111111111111001
3 8 11 45 2025 11111101001
4 13 17 362 131044 11111111111100100
5 16 21 1241 1540081 101110111111111110001
CROSSREFS
A357657 are the corresponding square roots of the record-setting squares.
Sequence in context: A010216 A302456 A303238 * A166522 A206610 A250031
KEYWORD
nonn,base,hard,more
AUTHOR
STATUS
approved