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Search: id:A114950
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| A114950 |
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A quartic quadratic recurrence. |
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+0
1
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| 1, 1, 2, 83525, 48670514501156640914, 5611303368570568119463158581109807779153712597124269146443734128560476495542441
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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) 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, 3. Semiprimes in this sequence include a(n) for n = 5.
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FORMULA
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a(0) = a(1) = 1, for n>1 a(n) = a(n-2)^4 + a(n-1)^2.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A000283, A112969, A114793.
Sequence in context: A100266 A071067 A060069 this_sequence A003840 A122540 A167518
Adjacent sequences: A114947 A114948 A114949 this_sequence A114951 A114952 A114953
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2006
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