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A344603
Triangular numbers whose Hamming weight is also triangular.
3
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
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
KEYWORD
nonn,base
AUTHOR
Michel Marcus, May 24 2021
STATUS
approved