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Search: id:A119996
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| A119996 |
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Numerator of Sum[ 1 / ( Fibonacci[k] * Fibonacci[k+2] ),{k,1,n}]. |
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+0
2
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| 1, 5, 14, 39, 103, 272, 713, 1869, 4894, 12815, 33551, 87840, 229969, 602069, 1576238, 4126647, 10803703, 28284464, 74049689, 193864605, 507544126, 1328767775, 3478759199, 9107509824, 23843770273, 62423800997, 163427632718
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OFFSET
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1,2
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COMMENT
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Prime p divides a(p-1) for p = {11,19,29,31,41,59,61,71,79,89,101,109,...} = A045468[n] Primes congruent to {1, 4} mod 5 or (except for the first term =5) A064739[n] Primes p such that Fibonacci(p)-1 is divisible by p. Prime p divides a((p-1)/2) for p = {5,7,29,41,61,89,101,109,149,181,229,241,269,281,349,389,401,409,421,449,461,509,521,541,...} Primes congruent to 1, 5, 9 (mod 20) or only Prime Norms of prime elements of Z[sqrt(-5)] A091729[n] (excluding squares). Prime p divides a((p-1)/3) for p = {13,23,41,139,151,199,331,541,...}.
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FORMULA
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a(n) = Numerator[Sum[1/(Fibonacci[k]*Fibonacci[k+2]),{k,1,n}]].
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MAPLE
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with(combinat): seq(fibonacci(n)*fibonacci(n+1)-1, n=2..28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
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MATHEMATICA
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Numerator[Table[Sum[1/(Fibonacci[k]*Fibonacci[k+2]), {k, 1, n}], {n, 1, 50}]]
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CROSSREFS
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Cf. A000045, A059248, A064831, A001654, A045468, A064739, A091729.
Adjacent sequences: A119993 A119994 A119995 this_sequence A119997 A119998 A119999
Sequence in context: A045553 A111715 A024525 this_sequence A027089 A023871 A122485
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 03 2006
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