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 A185128 Larger member of a pair of triangular numbers whose sum and difference are triangular. 7
 21, 171, 703, 990, 3741, 4186, 6786, 8778, 30628, 38781, 77028, 188191, 203203, 219453, 318801, 359128, 416328, 678030, 763230, 928203, 1023165, 1342341, 1505980, 1983036, 2114596, 2185095, 2349028, 2795430, 3219453, 3744216, 4928230, 6049981, 7036876, 7478778 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, nr. 8. LINKS FORMULA a(n) = A000217(A185223(n)). - R. J. Mathar, Feb 11 2018 EXAMPLE a(2) = 171, since the pair of triangular numbers 171 = 18*(18+1)/2 and 105 = 14*(14+1)/2 produce the sum 276 = 23*(23+1)/2 and the difference 66 = 11*(11+1)/2 which are both triangular numbers. MATHEMATICA Module[{trs=Accumulate[Range[3900]]}, Union[Select[Sort/@Subsets[trs, {2}], AllTrue[{Sqrt[8Total[#]+1], Sqrt[8Abs[#[[1]]-#[[2]]]+1]}, OddQ]&]]][[All, 2]]//Sort (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 02 2018 *) PROG (PARI) lista(nn) = {v = vector(nn, n, n*(n+1)/2); for (n=2, nn, for (k=1, n-1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]-v[k], 3), print1(v[n], ", ")); ); ); } \\ Michel Marcus, Jan 08 2015 CROSSREFS Cf. A000217, A185129, A185223, A185233, A185243, A185253, A185257, A185258. Sequence in context: A125358 A126516 A241219 * A007261 A119105 A015880 Adjacent sequences:  A185125 A185126 A185127 * A185129 A185130 A185131 KEYWORD nonn AUTHOR Martin Renner, Jan 20 2012 STATUS approved

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Last modified June 12 14:32 EDT 2021. Contains 344957 sequences. (Running on oeis4.)