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A069752
Smallest k>n such that the triangular number n*(n+1)/2 divides the triangular number k*(k+1)/2.
2
2, 3, 8, 15, 9, 14, 48, 63, 35, 44, 32, 39, 77, 20, 80, 255, 135, 152, 75, 35, 77, 230, 183, 200, 299, 324, 188, 203, 144, 155, 960, 351, 153, 84, 224, 296, 665, 246, 104, 615, 245, 258, 472, 99, 414, 1034, 704, 735, 1175, 374, 272, 636, 1377, 539, 175, 399, 551
OFFSET
1,1
COMMENTS
Note that k <= n^2-1, with equality occurring only if n and n+1 are a prime and a power of 2 (in either order); that is, when n is a Mersenne prime or n+1 is a Fermat prime. - T. D. Noe, Apr 08 2011
MATHEMATICA
Clear[k]; Join[{2}, Table[Reduce[k*(k+1) == 0, k, Modulus -> n*(n+1)][[3, 2]], {n, 2, 100}]] (* T. D. Noe, Apr 08 2011 *)
PROG
(PARI) for(s=1, 1000, s1=s*(s+1); n=s+1; while(n*(n+1)%s1>0, n++); print1(n, ", "); ) \\ Zak Seidov, Apr 08 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 01 2002
STATUS
approved