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A258967 a(1)=1, a(2)=2, a(3)=3, a(n) = ceiling(sqrt(a(n-1)*a(n-2)*a(n-3))), n>3. 0
1, 2, 3, 3, 5, 7, 11, 20, 40, 94, 275, 1017, 5128, 37871, 444415, 9290130, 395420005, 40404949540, 12183091294648, 13951642918891149, 82872169787001239679, 3753148776564192982863648, 2083123034674803589767277778236 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..23.

FORMULA

a(n) is approximately k^(c^n), where c is the real root of x^3 - (x^2 + x + 1)/2 = 0 equal to (1 + (64 - 3*sqrt(417))^(1/3) + (64 + 3*sqrt(417))^(1/3))/6, and k is approximately 1.7450496...

EXAMPLE

a(4) = ceiling(sqrt(1*2*3)) = 3;

a(5) = ceiling(sqrt(2*3*3)) = 5;

a(6) = ceiling(sqrt(3*3*5)) = 7.

MATHEMATICA

RecurrenceTable[{a[n] == Ceiling[Sqrt[a[n - 1] a[n - 2] a[n - 3]]], a[1] == 1, a[2] == 2, a[3] == 3}, a, {n, 1, 23}] (* Michael De Vlieger, Jul 02 2015 *)

a[1] = 1; a[2] = 2; a[3] = 3; a[n_] := a[n] = Ceiling[ Sqrt[ a[n - 1]*a[n - 2]*a[n - 3]]]; Array[a, 23] (* Robert G. Wilson v, Aug 12 2015 *)

PROG

(MAGMA) I:=[1, 2, 3]; [n le 3 select I[n] else Ceiling(Sqrt(Self(n-1)*Self(n-2)*Self(n-3))): n in [1..23]];

(PARI) first(m)={my(v=vector(m)); v[1]=1; v[2]=2; v[3]=3; for(i=4, m, v[i]=ceil(sqrt(v[i-1]*v[i-2]*v[i-3]))); v; } \\ Anders Hellström, Aug 20 2015

CROSSREFS

Cf. A258875, A254400.

Sequence in context: A241378 A226275 A035066 * A290000 A035068 A153643

Adjacent sequences:  A258964 A258965 A258966 * A258968 A258969 A258970

KEYWORD

nonn

AUTHOR

Morris Neene, Jun 15 2015

STATUS

approved

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Last modified November 18 17:33 EST 2019. Contains 329287 sequences. (Running on oeis4.)