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A219161 Recurrence equation a(n+1) = a(n)^3 - 3*a(n) with a(0) = 5. 6
5, 110, 1330670, 2356194280407770990, 13080769480548649962914459850235688797656360638877986030 (list; graph; refs; listen; history; text; internal format)
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), 644-646.

N. J. Fine, Infinite products for k-th roots, Amer. Math. Monthly Vol. 84, No. 8, Oct. 1977, 629-630.

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 n-th 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[#^3-3#&, 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

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Last modified February 18 15:30 EST 2020. Contains 332019 sequences. (Running on oeis4.)