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A114957
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A 4/3-power Fibonacci sequence.
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0
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1, 1, 2, 4, 9, 26, 96, 517, 4589, 80409, 3546873, 544383737, 445042712531, 3398279290987133, 510914600201184438040, 4084427005585662985398294639, 6528922582874884079540382952631569851, 12202683821888699966029264978793346242448495941305
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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) analogue of the Fibonacci sequence similarly to A000283 being the quadratic analogue 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.
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FORMULA
| a(0) = a(1) = 1, for n>1 a(n) = Ceiling[a(n-1)^(4/3) + a(n-2)^(4/3)].
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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.
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MATHEMATICA
| Nest[Append[#, Ceiling[Total[Take[#, -2]^(4/3)]]]&, {1, 1}, 17] (* From Harvey P. Dale, Apr 21 2011 *)
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CROSSREFS
| Cf. A000283, A112961, A112969, A114793.
Sequence in context: A188669 A087378 A004252 * A002773 A112706 A110138
Adjacent sequences: A114954 A114955 A114956 * A114958 A114959 A114960
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2006
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EXTENSIONS
| Corrected and extended by Harvey P. Dale, Apr 21 2011.
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