A182758 a(1) = 1, a(2) = 2, for n >= 3; a(n) = the smallest number h > a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + a(n)] * [a(n-1) + a(n)]] / [a(n-2) + a(n-1) + a(n)] is an integer.

1, 2, 3, 5, 7, 8, 9, 17, 25, 28, 47, 65, 70, 75, 105, 120, 125, 130, 135, 185, 220, 255, 273, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Example

For n = 5; a(3) = 3, a(4) = 5, a(5) = 7 before [(3+5)*(3+7)*(5+7)]  / (3+5+7) = 64 (integer).

Mathematica

nxt[{a_, b_}]:=Module[{h=b+1}, While[!IntegerQ[((a+b)(a+h)(b+h))/ (a+b+h)], h++]; {b, h}]; Transpose[NestList[nxt, {1, 2}, 40]][[1]] (* Harvey P. Dale, Dec 13 2012 *)

Prog

(Sage)
works = lambda a, h: ((a[-2]+a[-1])*(a[-2]+h)*(a[-1]+h)/(a[-2]+a[-1]+h)).is_integral()
a = [1, 2]
for n in range(3, 100):
    a += [next(h for h in IntegerRange(a[-1]+1, infinity) if works(a, h))]
print(a)
# D. S. McNeil, Nov 28 2010

Crossrefs

Cf. A182759.

Sequence in context: A171614 A029601 A290985 * A274768 A272667 A076385

Adjacent sequences: A182755 A182756 A182757 * A182759 A182760 A182761

Keyword

nonn

Author

Jaroslav Krizek, Nov 28 2010

Extensions

More terms from Harvey P. Dale, Dec 13 2012

Status

approved