

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
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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

R. J. Mathar, Table of n, a(n) for n = 1..58


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, n1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]v[k], 3), print1(n, ", ")); ); ); } \\ Michel Marcus, Jan 08 2015


CROSSREFS

Cf. A000217, A185128, A185129, A185233, A185243, A185253, A185257, A185258.
Sequence in context: A276480 A180438 A202366 * A299272 A101853 A132432
Adjacent sequences: A185220 A185221 A185222 * A185224 A185225 A185226


KEYWORD

nonn


AUTHOR

Martin Renner, Jan 20 2012


STATUS

approved



