A212315 Numbers m such that B(m) = B(triangular(m)), where B(m) is the binary weight of m (A000120).

0, 1, 3, 7, 15, 31, 39, 45, 63, 78, 79, 91, 93, 127, 139, 143, 158, 159, 175, 182, 187, 189, 222, 255, 286, 287, 318, 319, 351, 367, 375, 379, 381, 407, 446, 487, 511, 535, 543, 572, 574, 575, 607, 627, 638, 639, 703, 724, 727, 731, 747, 750, 759, 763, 765, 799, 823, 830

Offset: 1

Author

Alex Ratushnyak, Oct 24 2013

Keywords

• nonn
• base
• easy

Links

• Dumitru Damian, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A077436, A083567, A118655, A212314.

Programs

Python

def isa(n): return n.bit_count()==((n*(n+1))>>1).bit_count()
print(list(n for n in range(10**3) if isa(n)))  # Dumitru Damian, Mar 04 2023

Formula

A000120(a(n)) = A000120(a(n)*(a(n)+1)/2).