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Search: id:A093062
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| A093062 |
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Fibonacci[Prime[i]]-Prime[Fibonacci[i]]. |
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+0
2
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| -1, 0, 2, 8, 78, 214, 1556, 4108, 28518, 513972, 1345808, 24156990, 165578670, 433491846, 2971210580, 53316283380, 956722012572, 2504730758802, 44945570173074, 308061521102198, 806515532933562, 14472334024479534, 99194853094422264, 1779979416004150202
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Composition of Prime[ ] and Fibonacci[ ] is not commutative. Does a prime p ever divide Fibonacci[Prime[p]]-Prime[Fibonacci[p]]?
Note that A093062(3) = 2 is the only prime element of the sequence. This is because after 2, all primes are even; and the Fibonacci number F(n) is even only for n = 3k for some integer k [which relates to the fact that A082115 Fibonacci sequence (mod 3) is periodic with Pisano period 8]. Hence after A093062(1) = -1, Fibonacci[Prime[n]]-Prime[Fibonacci[n]] is always the difference of two odd numbers, hence is even. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 23 2006
Is a[i] ever divisible by i? Answer yes. The quotient is an integer for i = 4, 28 and 30 through 63. - Dennis S. Kluk (mathemagician(AT)ameritech.net), Aug 16 2006
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,41
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FORMULA
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a(n) = Fibonacci[Prime[i]]-Prime[Fibonacci[i]]
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EXAMPLE
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a[11] = Fibonacci[Prime[11]]-Prime[Fibonacci[11]] = 1345808.
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MATHEMATICA
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For[i=1, i<61, i++, Print[i, " ", Fibonacci[Prime[i]]-Prime[Fibonacci[i]]]]
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PROGRAM
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(PARI) { default(primelimit, 4294965247); for(n=1, 41, a=fibonacci(prime(n)) - prime(fibonacci(n)); write("b093062.txt", n, " ", a); ); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 20 2009]
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CROSSREFS
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Cf. A000040, A000045.
Cf. A082115.
Sequence in context: A064605 A132039 A002668 this_sequence A057984 A071254 A063528
Adjacent sequences: A093059 A093060 A093061 this_sequence A093063 A093064 A093065
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KEYWORD
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easy,sign
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AUTHOR
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Dennis S. Kluk (mathemagician(AT)ameritech.net), May 08 2004
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