A348906 Squares with a square number of 1's in their binary expansion.

0, 1, 4, 16, 64, 169, 225, 256, 676, 900, 1024, 2209, 2704, 3600, 4096, 5625, 7921, 8836, 10201, 10816, 12321, 13689, 14400, 16384, 19321, 20449, 22201, 22500, 23409, 26569, 27889, 28561, 29929, 30625, 31684, 32041, 35344, 38809, 40401, 40804, 43264, 49284, 52441

Offset: 1

Author

Ctibor O. Zizka, Nov 03 2021

Keywords

• nonn
• base

Comments

If a number k is of the form 2^(2*r), r >= 0, then k is included in this sequence.

Examples

			225 is in the sequence because it is a square and the number of 1's in the binary expansion of 225 is 4 which is a square.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000290 and A084561.

Cf. A000120, A081092, A344603.

Programs

Maple

q:= n-> issqr(add(i, i=Bits[Split](n))):
select(q, [i^2$i=0..250])[];  # Alois P. Heinz, Nov 03 2021

Mathematica

Select[Range[0, 300]^2, IntegerQ @ Sqrt[DigitCount[#, 2, 1]] &] (* Amiram Eldar, Nov 03 2021 *)

PARI

isok(k) = issquare(k) && issquare(hammingweight(k)); \\ Michel Marcus, Nov 03 2021