A344603 Triangular numbers whose Hamming weight is also triangular.

0, 1, 21, 28, 190, 231, 276, 378, 435, 630, 741, 903, 946, 1326, 1540, 1596, 1830, 1953, 2016, 2278, 2701, 4278, 4465, 5460, 5778, 5886, 6328, 6441, 6670, 6903, 8646, 11026, 11781, 11935, 12246, 12720, 15225, 15400, 15931, 16471, 17391, 17578, 17955, 18336, 20100

Offset: 1

Author

Michel Marcus, May 24 2021

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• Audrey Baumheckel and Tamás Forgács, Guided by the primes -- an exploration of very triangular numbers, arXiv:2105.10354 [math.HO], 2021.

Crossrefs

Cf. A000120.

Intersection of A000217 and A344602.

Programs

Maple

q:= n-> issqr(8*add(i, i=Bits[Split](n))+1):
select(q, [j*(j+1)/2$j=0..200])[];  # Alois P. Heinz, May 24 2021

Mathematica

Select[Table[n*(n + 1)/2, {n, 0, 200}], IntegerQ @ Sqrt[8 * Plus @@ IntegerDigits[#, 2] + 1] &] (* Amiram Eldar, May 24 2021 *)
Select[Accumulate[Range[0,200]],OddQ[Sqrt[8 DigitCount[#,2,1]+1]]&] (* Harvey P. Dale, Feb 19 2023 *)

PARI

isok(n) = ispolygonal(n, 3) && ispolygonal(hammingweight(n), 3);