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A323066 Numbers whose binary complement (A035327) is a square. 1

%I #20 Sep 03 2021 12:11:20

%S 0,1,2,3,6,7,11,14,15,22,27,30,31,38,47,54,59,62,63,78,91,102,111,118,

%T 123,126,127,134,155,174,191,206,219,230,239,246,251,254,255,286,315,

%U 342,367,390,411,430,447,462,475,486,495,502,507,510,511,539,582,623,662

%N Numbers whose binary complement (A035327) is a square.

%C The binary complement of every square is in the sequence. Using that might ease computation. - _David A. Corneth_, Jan 08 2019

%e The binary complement of 22 is 9. Because 9 is a square, 22 is in the sequence.

%e The binary complement of 4^2 = 16 is 15 so 15 is in the sequence. - _David A. Corneth_, Jan 08 2019

%p q:= n-> issqr(Bits[Nand](n$2)):

%p select(q, [$0..1000])[]; # _Alois P. Heinz_, Sep 03 2021

%t Select[Range@ 700, IntegerQ@ Sqrt@ FromDigits[IntegerDigits[#, 2] /. {0 -> 1, 1 -> 0}, 2] &] (* _Michael De Vlieger_, Jan 04 2019 *)

%o (PARI) bc(n) = bitxor(n, 2^(1+logint(max(n, 1), 2))-1); \\ A035327

%o isok(n) = issquare(bc(n)); \\ _Michel Marcus_, Jan 04 2019

%Y Cf. A035327, A000290, A000225 is a subsequence.

%K nonn,easy,base

%O 1,3

%A _Alex Ratushnyak_, Jan 03 2019

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)