A357304 Records of the Hamming weight of squares.

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 87, 88, 89

Offset: 1

Author

Hugo Pfoertner, Oct 01 2022

Keywords

• nonn
• hard

Examples

			a(70) = 77 corresponds to A230097(70) = 34895284158283. Its square 1217680856487316499797508089 is the smallest and the only 90-bit square with this Hamming weight.
		

Crossrefs

A230097 gives the values of k such that A000120(k^2) sets a new record.

Cf. A000120, A000290, A159918, A357658.

Extensions

Missing a(68)=75 and a(71)-a(80) from Bert Dobbelaere, Nov 20 2022