A112982 a(1) = a(2) = a(3) = a(4) = 1; for n>4: a(n) = a(n-1)^4 + a(n-2)^4 + a(n-3)^4 + a(n-4)^4.

1, 1, 1, 1, 4, 259, 4499860819, 410011770879070587605284428972195139939

Offset

1,5

Comments

A quartic tetranacci sequence.

This is a quartic (biquadratic) analog of a tetranacci sequence A000288, similarly to A000283 being the quadratic analog of the Fibonacci sequence A000045. a(5), a(6) a(7) and a(8) are semiprime. a(9) has 155 digits.

Links

Indranil Ghosh, Table of n, a(n) for n = 1..10

Eric Weisstein's World of Mathematics, Quartic Equation.

Example

a(5) = 1^4 + 1^4 + 1^4 + 1^4 = 4.
a(6) = 1^4 + 1^4 + 1^4 + 4^4 = 259.
a(7) = 1^4 + 1^4 + 4^4 + 259^4 = 4499860819.
a(8) = 1^4 + 4^4 + 259^4 + 4499860819^4.

Mathematica

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1, a[n]==a[n-1]^4+ a[n-2]^4+ a[n-3]^4+ a[n-4]^4}, a, {n, 10}] (* Harvey P. Dale, May 19 2019 *)

Crossrefs

Cf. A000045, A000283, A000288.

Sequence in context: A068417 A116967 A003382 * A352332 A061788 A203839

Adjacent sequences: A112979 A112980 A112981 * A112983 A112984 A112985

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 03 2006

Status

approved