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a(n) is the least number of binary zeros of squares with binary weight n.
3

%I #31 Oct 13 2022 16:33:35

%S 1,0,2,2,4,2,3,4,3,4,5,5,5,2,5,5,5,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,8,7,

%T 6,8,9,6,7,8,9,8,9,9,8,10,9,9,10,9,9,9,9,10,10,10,11,10

%N a(n) is the least number of binary zeros of squares with binary weight n.

%H Karl-Heinz Hofmann, <a href="/A356878/a356878.txt">Table (like in example) with n = 0..57</a>

%e Squares with | possible number of zeros

%e binary weight | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e n | the leftmost value is a(n)

%e -----------------+----------------------------------------------------

%e 0 | - 1 - - - - - - - - - - - - - - -

%e 1 | 0 - 2 - 4 - 6 - 8 - 10 - 12 - 14 - ...

%e 2 | - - 2 - 4 - 6 - 8 - 10 - 12 - 14 - ...

%e 3 | - - 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e 4 | - - - - 4 - 6 - 8 - 10 - 12 - 14 - ...

%e 5 | - - 2 - 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e 6 | - - - 3 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e 7 | - - - - 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e 8 | - - - 3 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e 9 | - - - - 4 5 6 7 8 9 10 11 12 13 14 15 ...

%e 10 | - - - - - 5 6 7 8 9 10 11 12 13 14 15 ...

%e 11 | - - - - - 5 6 7 8 9 10 11 12 13 14 15 ...

%e 12 | - - - - - 5 6 7 8 9 10 11 12 13 14 15 ...

%e 13 | - - 2 - 4 - 6 7 8 9 10 11 12 13 14 15 ...

%e 14 | - - - - - 5 6 7 8 9 10 11 12 13 14 15 ...

%e : | ...

%Y Cf. A000120, A164343, A164344.

%K nonn,base,hard,more

%O 0,3

%A _Karl-Heinz Hofmann_, Sep 30 2022