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

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