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

Author

Jonathan Vos Post, Jan 03 2006

Keywords

• easy
• nonn

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.

Examples

			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.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10
• Eric Weisstein's World of Mathematics, Quartic Equation.

Crossrefs

Cf. A000045, A000283, A000288.

Programs

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 *)