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A219163 Recurrence equation a(n+1) = a(n)^4 - 4*a(n)^2 + 2 with a(0) = 4. 3
4, 194, 1416317954, 4023861667741036022825635656102100994 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Bisection of A003010.

a(4) has 147 digits and a(5) has 586 digits. - Harvey P. Dale, Mar 03 2020

LINKS

Table of n, a(n) for n=0..3.

FORMULA

Let alpha = 2 + sqrt(3). Then a(n) = (alpha)^(4^n) + (1/alpha)^(4^n).

a(n) = A003010(2*n) = A003500(4^n).

Product {n >= 0} ((1 + 2/a(n))/(1 - 2/a(n)^2)) = sqrt(3).

MATHEMATICA

NestList[#^4-4#^2+2&, 4, 5] (* Harvey P. Dale, Mar 03 2020 *)

PROG

(PARI) a(n)={if(n==0, 4, a(n-1)^4-4*a(n-1)^2+2)} \\ Edward Jiang, Sep 11 2014

CROSSREFS

Cf. A001999, A003010, A003500, A219162, A219164, A219165.

Sequence in context: A159783 A028370 A042127 * A017546 A144044 A221197

Adjacent sequences:  A219160 A219161 A219162 * A219164 A219165 A219166

KEYWORD

nonn,easy

AUTHOR

Peter Bala, Nov 13 2012

STATUS

approved

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)