A112980 a(0) = 0, a(1) = 1; for n>=2: a(n) = a(n-1)^5 + a(n-2)^5.

0, 1, 1, 2, 33, 39135425, 91801604643057285538237803582627026018

Offset

0,4

Comments

A quintic Fibonacci sequence.

This is the quintic analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. In base 10, n^5 has the same rightmost digit as n. a(7) has 190 digits.

Links

Table of n, a(n) for n=0..6.

Eric Weisstein's World of Mathematics, Quintic Equation.

Example

a(3) = 1^5 + 1^5 = 2.
a(4) = 1^5 + 2^5 = 33.
a(5) = 2^5 + 33^5 = 39135425.
a(6) = 33^5 + 39135425^5 = 91801604643057285538237803582627026018.

Mathematica

RecurrenceTable[{a[1]==a[2]==1, a[n]==a[n-1]^5+a[n-2]^5}, a, {n, 7}] (* Harvey P. Dale, May 01 2012 *)

Crossrefs

Cf. A000045, A000283.

Sequence in context: A132519 A117969 A003820 * A109336 A180342 A343905

Adjacent sequences: A112977 A112978 A112979 * A112981 A112982 A112983

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 02 2006

Extensions

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

Status

approved