

A114950


A quartic quadratic recurrence.


0




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(n1)^4 + a(n2)^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(n1)^4 + a(n2)^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[n1]^4 + a[n2]^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



