A350368 Triangular numbers that are the sum of two distinct nonzero triangular numbers in exactly two ways.

231, 1081, 1225, 1431, 1711, 2556, 5356, 7381, 7875, 8256, 15931, 19306, 20706, 26106, 30381, 33153, 36856, 46056, 51681, 75078, 78606, 102831, 104653, 135981, 149331, 153181, 182106, 197506, 225456, 263175, 265356, 316410, 317206, 336610, 379756, 424581

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

231 = 21 + 210 = 78 + 153.
1081 = 91 + 990 = 378 + 703.

Mathematica

(P=PolygonalNumber)[3, Select[Range@200, Length@Select[Subsets[P[3, Range[s=#]], {2}], Total@#==P[3, s]&]==2&]] (* Giorgos Kalogeropoulos, Dec 31 2021 *)

Prog

(Python)
from collections import Counter
from itertools import count, takewhile, combinations as combs
def aupto(limit):
    tris = takewhile(lambda x: x <= limit, (k*(k+1)//2 for k in count(1)))
    trilst = list(tris); triset = set(trilst)
    tri2ct = Counter(sum(c) for c in combs(trilst, 2) if sum(c) in triset)
    return sorted(t for t in tri2ct if t <= limit and tri2ct[t] == 2)
print(aupto(500000)) # Michael S. Branicky, Dec 27 2021

Crossrefs

Intersection of A000217 and A265134.

Sequence in context: A246886 A258167 A287472 * A183672 A183664 A260302

Adjacent sequences: A350365 A350366 A350367 * A350369 A350370 A350371

Keyword

nonn

Author

Shyam Sunder Gupta, Dec 27 2021

Status

approved