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A185223
Side of triangle of larger member of a pair of triangular numbers whose sum and difference are triangular.
8
6, 18, 37, 44, 86, 91, 116, 132, 247, 278, 392, 613, 637, 662, 798, 847, 912, 1164, 1235, 1362, 1430, 1638, 1735, 1991, 2056, 2090, 2167, 2364, 2537, 2736, 3139, 3478, 3751, 3867, 4298, 4422, 4553, 5202, 6068, 6391, 6500, 7241, 7859, 7957, 8378, 9309, 9793
OFFSET
1,1
COMMENTS
Side lengths where both triangular numbers are the same (A053141) are not included. - R. J. Mathar, Feb 11 2018
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, nr. 8.
LINKS
EXAMPLE
a(2) = 18, 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.
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(n, ", ")); ); ); } \\ Michel Marcus, Jan 08 2015
KEYWORD
nonn
AUTHOR
Martin Renner, Jan 20 2012
STATUS
approved