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Search: id:A072523
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| A072523 |
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Sum of remainders when n-th Fibonacci number is divided by all smaller Fibonacci numbers > 1. |
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+0
2
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| 0, 0, 0, 1, 3, 5, 10, 15, 28, 46, 79, 120, 207, 330, 540, 867, 1428, 2293, 3737, 6009, 9778, 15808, 25630, 41370, 67092, 108483, 175649, 284022, 459938, 743945, 1204113, 1947712, 3152386, 5100237, 8253262, 13352465, 21607324, 34959920
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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Conjecture: lim n->inf F(n)/a(n) = sqrt(5)/2 where F(n) is the n-th Fibonacci number and therefore lim n->inf a(n)/a(n-1) = Phi (i.e. (sqrt(5)+1)/2 or lim n->inf F(n)/F(n-1)) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jul 14 2004
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EXAMPLE
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The eighth Fibonacci number is 21; division by 2, 3, 5, 8,13 gives the remainders 1, 0, 1, 5, 8, so a(8) = 1 + 0 + 1+ 5 + 8 = 15.
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PROGRAM
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(PARI) for(n=1, 38, s=0; for(j=3, n-1, s=s+fibonacci(n)%fibonacci(j)); print1(s, ", "))
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CROSSREFS
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Sequence in context: A045513 A008337 A077285 this_sequence A054473 A006168 A037246
Adjacent sequences: A072520 A072521 A072522 this_sequence A072524 A072525 A072526
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 31 2002
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 02 2002
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