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

Author

Jonathan Vos Post, Jan 02 2006

Keywords

• easy
• nonn

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).

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Quartic Equation.

Crossrefs

Cf. A000045, A000283.

Programs

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 *)

Formula

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

Extensions

Name edited by Petros Hadjicostas, Nov 03 2019

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