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.

1, 2, 3, 3, 5, 7, 11, 20, 40, 94, 275, 1017, 5128, 37871, 444415, 9290130, 395420005, 40404949540, 12183091294648, 13951642918891149, 82872169787001239679, 3753148776564192982863648, 2083123034674803589767277778237, 25454214863632278822694894280883452911

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..39

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 *)
nxt[{a_, b_, c_}]:={b, c, Ceiling[Sqrt[a*b*c]]}; NestList[nxt, {1, 2, 3}, 30][[All, 1]] (* Harvey P. Dale, Sep 09 2021 *)

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 * A035068 A153643 A053218

Adjacent sequences: A258964 A258965 A258966 * A258968 A258969 A258970

Keyword

nonn

Author

Morris Neene, Jun 15 2015

Extensions

Corrected and extended by Harvey P. Dale, Sep 09 2021

Status

approved