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A160757
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Averages of the Fibonacci numbers which take integer values.
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1
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1, 1, 5058, 262213938, 18124577012898, 187952389930860, 1409394295257361938, 116903055445824294157698, 10100618828005365858877129458, 81435914480042681825934186407384633298, 7505278652741640947693896415563573183203138, 700346071081054203480884565881868806176873272498
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The numbers n such that F(1)+F(2)+...+F(n)=F(n+2)-1 is divisible by n are given in A111035. [From Max Alekseyev (maxale(AT)gmail.com), Jun 04 2009]
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FORMULA
| 1/n*Sum {j=1..n} Fibonacci_j is an integer.
a(n) = (A000045(A111035(n)+2)-1) / A111035(n) = A000071(A111035(n)+2) / A111035(n) [From Max Alekseyev (maxale(AT)gmail.com), Jun 04 2009]
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MATHEMATICA
| lst = {}; Do[a = Sum[ Fibonacci@ j, {j, n}]/n; If[ IntegerQ@ a, AppendTo[lst, a]], {n, 250}]; lst
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CROSSREFS
| Cf. A050248, integer average of n primes for some n, A000045.
Sequence in context: A155145 A187356 A187354 * A046169 A058908 A116887
Adjacent sequences: A160754 A160755 A160756 * A160758 A160759 A160760
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KEYWORD
| easy,nonn
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AUTHOR
| Daniel Tisdale (daniel6874(AT)gmail.com), May 25 2009
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EXTENSIONS
| Corrected and extended by Max Alekseyev (maxale(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 04 2009
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