A357656 - OEIS

A357656

a(n) is a lower bound for the largest Hamming weight of squares with exactly n binary zeros.

1, 0, 13, 8, 13, 16, 37, 38, 44

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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.

LINKS

Table of n, a(n) for n=0..8.

EXAMPLE

A357657(n)

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.

Cf. A000120, A000290, A159918, A230097, A356878, A357304, A357305.

Sequence in context: A010216 A302456 A303238 * A166522 A206610 A250031

Adjacent sequences: A357653 A357654 A357655 * A357657 A357658 A357659

KEYWORD

nonn,base,hard,more

AUTHOR

Karl-Heinz Hofmann and Hugo Pfoertner, Oct 07 2022

STATUS

approved