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A185128
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Larger member of a pair of triangular numbers whose sum and difference are triangular.
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7
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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
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OFFSET
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1,1
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REFERENCES
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Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, nr. 8.
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LINKS
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FORMULA
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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