

A114957


A 4/3power Fibonacci sequence.


0



1, 1, 2, 4, 9, 26, 96, 517, 4589, 80409, 3546873, 544383737, 445042712531, 3398279290987133, 510914600201184438040, 4084427005585662985398294639, 6528922582874884079540382952631569851, 12202683821888699966029264978793346242448495941305
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OFFSET

0,3


COMMENTS

This sequence is related to: A112961 "a cubic Fibonacci sequence" a(1) = a(2) = 1; for n>2: a(n) = a(n1)^3 + a(n2)^3 A112969 "a 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. Semiprimes in this sequence include a(n) for n = 3, 4, 5, 7, 8.


LINKS

Table of n, a(n) for n=0..17.


FORMULA

a(0) = a(1) = 1, for n>1 a(n) = ceiling(a(n1)^(4/3) + a(n2)^(4/3)).


EXAMPLE

a(2) = ceiling(a(0)^(4/3) + a(1)^(4/3)) = ceiling(1^(4/3) + 1^(4/3)) = 2.
a(3) = ceiling(a(1)^(4/3) + a(2)^(4/3)) = ceiling)1^(4/3) + 2^(4/3)) = ceiling(3.5198421) = 4.
a(4) = ceiling(2^(4/3) + 4^(4/3)) = ceiling(8.86944631) = 9.
a(5) = ceiling(4^(4/3) + 9^(4/3)) = ceiling(25.0703586) = 26.
a(6) = ceiling(9^(4/3) + 26^(4/3)) = ceiling(95.7456522) = 96.
a(7) = ceiling(26^(4/3) + 96^(4/3)) = ceiling(516.595167) = 517.
a(8) = ceiling(96^(4/3) + 517^(4/3)) = ceiling(4588.99022) = 4589.


MATHEMATICA

Nest[Append[#, Ceiling[Total[Take[#, 2]^(4/3)]]]&, {1, 1}, 17] (* Harvey P. Dale, Apr 21 2011 *)


CROSSREFS

Cf. A000283, A112961, A112969, A114793.
Sequence in context: A243568 A087378 A004252 * A002773 A112706 A110138
Adjacent sequences: A114954 A114955 A114956 * A114958 A114959 A114960


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 21 2006


EXTENSIONS

Corrected and extended by Harvey P. Dale, Apr 21 2011


STATUS

approved



