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A182752
a(1) = 1, a(2) = 6, for n >= 3; a(n) = the smallest number greater than 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.
7
1, 6, 14, 84, 196, 1176, 2744, 16464, 38416, 230496, 537824, 3226944, 7529536, 45177216, 105413504, 632481024, 1475789056, 8854734336, 20661046784
OFFSET
1,2
FORMULA
a(2n) = 6 * a(2n-1), a(2n+1) = 7/3 * a(2n).
G.f.: (1 + 6*x)/(1 - 14*x^2). - Georg Fischer, Nov 17 2022
EXAMPLE
a(5)=196 since (14+84)*(14+x)*(84+x)/(14*84*x) is an integer for x=196, but not an integer for any x satisfying 85 <= x <= 195.
MATHEMATICA
nxt[{n_, a_}]:={n+1, If[OddQ[n], 6*a, 7/3 a]}; NestList[nxt, {1, 1}, 20][[All, 2]] (* Harvey P. Dale, Aug 14 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Nov 27 2010
STATUS
approved