

A219161


Recurrence equation a(n+1) = a(n)^3  3*a(n) with a(0) = 5.


6




OFFSET

0,1


COMMENTS

For some general remarks on this recurrence see A001999.
The next term (a(5)) has 166 digits.  Harvey P. Dale, Apr 23 2019


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..6
E. B. Escott, Rapid method for extracting a square root, Amer. Math. Monthly, 44 (1937), 644646.
N. J. Fine, Infinite products for kth roots, Amer. Math. Monthly Vol. 84, No. 8, Oct. 1977, 629630.


FORMULA

a(n) = (1/2*(5 + sqrt(21)))^(3^n) + (1/2*(5  sqrt(21)))^(3^n).
Product_{n = 0..inf} (1 + 2/(a(n)  1)) = sqrt(7/3).
a(n) = 2*T(3^n,5/2), where T(n,x) denotes the nth Chebyshev polynomial of the first kind. Cf. A001999.  Peter Bala, Feb 01 2017


MATHEMATICA

RecurrenceTable[{a[n] == a[n  1]^3  3*a[n  1], a[0] == 5}, a, {n,
0, 5}] (* G. C. Greubel, Dec 30 2016 *)
NestList[#^33#&, 5, 5] (* Harvey P. Dale, Apr 23 2019 *)


CROSSREFS

Cf. A001999, A112845, A219160.
Sequence in context: A203367 A322631 A294965 * A284461 A002400 A268404
Adjacent sequences: A219158 A219159 A219160 * A219162 A219163 A219164


KEYWORD

nonn,easy


AUTHOR

Peter Bala, Nov 13 2012


STATUS

approved



