A114950 A quartic quadratic recurrence.

1, 1, 2, 17, 83525, 48670514501156640914, 5611303368570568119463158581109807779153712597124269146443734128560476495542441

Offset

0,3

Comments

a(6) has 315 digits. This sequence is related to: A112969 "quartic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n-1)^4 + a(n-2)^4, which is the quartic (or biquadratic) analog of the Fibonacci sequence similarly to A000283 being the quadratic analog of the Fibonacci sequence. Primes in this sequence include a(n) for n = 2, 3. Semiprimes in this sequence include a(n) for n = 5.

Links

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

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Formula

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

a(n) ~ c^(4^n), where c = 1.045263645117629170027922399491730015846213509999461317320720034161754262379... . - Vaclav Kotesovec, Dec 18 2014

Example

a(2) = a(1)^4 + a(0)^2 = 1^4 + 1^2 = 2.
a(3) = a(2)^4 + a(1)^2 = 2^4 + 1^2 = 17.
a(4) = a(3)^4 + a(2)^2 = 17^4 + 2^2 = 83525.
a(5) = a(4)^4 + a(3)^2 = 83525^4 + 17^2 = 48670514501156640914.

Mathematica

RecurrenceTable[{a[0] ==1, a[1] == 1, a[n] == a[n-1]^4 + a[n-2]^2}, a, {n, 0, 8}] (* Vaclav Kotesovec, Dec 18 2014 *)

Crossrefs

Cf. A000283, A112969, A114793.

Sequence in context: A078624 A163319 A269836 * A112969 A208208 A290189

Adjacent sequences: A114947 A114948 A114949 * A114951 A114952 A114953

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 21 2006

Extensions

Formula corrected by Vaclav Kotesovec, Dec 18 2014

Missing a(3) added from Vaclav Kotesovec, Dec 18 2014

Status

approved