A185128 Larger member of a pair of triangular numbers whose sum and difference are triangular.

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

Offset

1,1

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, nr. 8.

Links

Table of n, a(n) for n=1..34.

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