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
KEYWORD
nonn
AUTHOR
Morris Neene, Jun 15 2015
EXTENSIONS
Corrected and extended by Harvey P. Dale, Sep 09 2021
STATUS
approved