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A114957 A 4/3-power Fibonacci sequence. 0
1, 1, 2, 4, 9, 26, 96, 517, 4589, 80409, 3546873, 544383737, 445042712531, 3398279290987133, 510914600201184438040, 4084427005585662985398294639, 6528922582874884079540382952631569851, 12202683821888699966029264978793346242448495941305 (list; graph; refs; listen; history; text; internal format)
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(n-1)^3 + a(n-2)^3 A112969 "a 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. 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(n-1)^(4/3) + a(n-2)^(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

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Last modified February 18 00:19 EST 2019. Contains 320237 sequences. (Running on oeis4.)