A112969 a(n) = a(n-1)^4 + a(n-2)^4 for n >= 2 with a(0) = 0, a(1) = 1.

0, 1, 1, 2, 17, 83537, 48698490414981559682, 5624216052381164150697569400035392464306474190030694298257552124199835791859537

Offset

0,4

Comments

A quartic Fibonacci sequence.

This is the quartic (or biquadratic) analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. The primes in this sequence begin a(3), a(4), a(5).

Links

Table of n, a(n) for n=0..7.

Eric Weisstein's World of Mathematics, Quartic Equation.

Formula

a(n) ~ c^(4^n), where c = 1.0111288972169538887655499395580320278253918666919181401824606983217263409... . - Vaclav Kotesovec, Dec 18 2014

Example

a(3) = 1^4 + 1^4 = 2.
a(4) = 1^4 + 2^4 = 17.
a(5) = 2^4 + 17^4 = 83537.
a(6) = 17^4 + 83537^4 = 48698490414981559682.

Mathematica

RecurrenceTable[{a[1] ==1, a[2] == 1, a[n] == a[n-1]^4 + a[n-2]^4}, a, {n, 1, 8}] (* Vaclav Kotesovec, Dec 18 2014 *)

Crossrefs

Cf. A000045, A000283.

Sequence in context: A163319 A269836 A114950 * A208208 A290189 A279883

Adjacent sequences: A112966 A112967 A112968 * A112970 A112971 A112972

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 02 2006

Extensions

Name edited by Petros Hadjicostas, Nov 03 2019

a(0)=0 prepended by Alois P. Heinz, Sep 15 2023

Status

approved