A331219 Positive numbers of the form u * v where the binary representations of u and of v have the same number of 0's and the same number of 1's.

1, 4, 9, 16, 25, 30, 36, 49, 64, 81, 90, 100, 108, 120, 121, 143, 144, 154, 169, 182, 196, 225, 256, 289, 306, 324, 340, 360, 361, 399, 400, 408, 418, 432, 441, 462, 475, 480, 484, 494, 525, 529, 532, 546, 550, 572, 576, 588, 616, 621, 625, 650, 667, 676, 690

Offset

1,2

Comments

In other words, the terms of this sequence are squares or the products of two binary anagrams.

Leading zeros are ignored.

If m belongs to the sequence, then 4*m also belongs to the sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

a(n) = A331266(n) * A331267(n).

Example

The binary representations of 5 and 6 are "101" and "110", respectively.
So 5 and 6 are binary anagrams, and 30 = 5*6 belongs to the sequence.

Prog

(PARI) is(n, base=2) = fordiv (n, d, if (vecsort(digits(d, base))==vecsort(digits(n/d, base)), return (1))); return (0)

Crossrefs

Cf. A331220 (ternary analog), A331221 (decimal analog), A331266, A331267.

Sequence in context: A086132 A010433 A175592 * A337534 A126589 A340585

Adjacent sequences: A331216 A331217 A331218 * A331220 A331221 A331222

Keyword

nonn,base

Author

Rémy Sigrist, Jan 12 2020

Status

approved