A182752 - OEIS

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.

1, 6, 14, 84, 196, 1176, 2744, 16464, 38416, 230496, 537824, 3226944, 7529536, 45177216, 105413504, 632481024, 1475789056, 8854734336, 20661046784

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OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,14).

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

Cf. A182751, A182753, A182754, A182755, A182756, A182757.

Sequence in context: A333103 A139257 A056842 * A200033 A219376 A130263

Adjacent sequences: A182749 A182750 A182751 * A182753 A182754 A182755

KEYWORD

nonn,easy

AUTHOR

Jaroslav Krizek, Nov 27 2010

STATUS

approved