A133653 - OEIS

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A133653

A007318^(-1) * A003261.

1, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154

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OFFSET

1,2

COMMENTS

It appears this sequence gives the positive integers m such that the sum of the first m Fibonacci numbers divides their product. For example, if n=2 and m=a(2)=6, we have the sum 1+1+2+3+5+8=20 which clearly divides the corresponding product 480. See A175553 for the analogous sequence when using the triangular numbers. Sum_{k=1..n} Fibonacci(k) divides Product_{k=1..n} Fibonacci(k). - John W. Layman, Jul 10 2010

LINKS

Table of n, a(n) for n=1..39.

FORMULA

Inverse binomial transform of A003261: (1, 7, 23, 63, 159, 383, ...).

Binomial transform of [1, 5, -1, 1, -1, 1, ...].

"1" followed by 2 * [3, 5, 7, 9, 11, ...].

O.g.f.: x*(1+4x-x^2)/(1-x)^2. a(n) = 4n-2, n > 1. - R. J. Mathar, Jun 08 2008

1/(1+1/(6+1/(10+1/(14+1/(...(continued fraction)))))) = (e-1)/2 with e = 2.718281...- Philippe Deléham, Mar 09 2013

EXAMPLE

a(4) = 14 = (1, 3, 3, 1) dot (1, 5, -1, 1) = (1, 15, -3, 1).

CROSSREFS

Cf. A003261, A007318, A175553.