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

1,3

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.

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 *)

Prog

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

Crossrefs

Cf. A000120.

Intersection of A000217 and A344602.

Sequence in context: A130202 A162692 A048067 * A212192 A166647 A119107

Adjacent sequences: A344600 A344601 A344602 * A344604 A344605 A344606

Keyword

nonn,base

Author

Michel Marcus, May 24 2021

Status

approved