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A350368
Triangular numbers that are the sum of two distinct nonzero triangular numbers in exactly two ways.
0
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
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
KEYWORD
nonn
AUTHOR
Shyam Sunder Gupta, Dec 27 2021
STATUS
approved