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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A357656 a(n) is a lower bound for the largest Hamming weight of squares with exactly n binary zeros.

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%I A357656 #7 Oct 13 2022 15:28:39
%S A357656 1,0,13,8,13,16,37,38,44
%N A357656 a(n) is a lower bound for the largest Hamming weight of squares with exactly n binary zeros.
%C A357656 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.
%C A357656 a(9) >= 63, a(10) >= 57.
%e A357656                 A357657(n)
%e A357656    n  a(n) bits     k       k^2          k^2 in binary
%e A357656    0    1    1      1         1                      1
%e A357656    1    0    1      0         0                      0
%e A357656    2   13   15    181     32761        111111111111001
%e A357656    3    8   11     45      2025            11111101001
%e A357656    4   13   17    362    131044      11111111111100100
%e A357656    5   16   21   1241   1540081  101110111111111110001
%Y A357656 A357657 are the corresponding square roots of the record-setting squares.
%Y A357656 Cf. A000120, A000290, A159918, A230097, A356878, A357304, A357305.
%K A357656 nonn,base,hard,more
%O A357656 0,3
%A A357656 _Karl-Heinz Hofmann_ and _Hugo Pfoertner_, Oct 07 2022