A133653 - OEIS

%I #16 Sep 01 2024 13:44:19

%S 1,6,10,14,18,22,26,30,34,38,42,46,50,54,58,62,66,70,74,78,82,86,90,

%T 94,98,102,106,110,114,118,122,126,130,134,138,142,146,150,154

%N A007318^(-1) * A003261.

%C 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

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

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

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

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

%F 1/(1+1/(6+1/(10+1/(14+1/(...(continued fraction)))))) = (e-1)/2 with e = 2.718281...- _Philippe Deléham_, Mar 09 2013

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

%Y Cf. A003261, A007318, A175553.

%Y Essentially the same as A130824, A113127, A111284, A073760, A016825.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Sep 19 2007

%E More terms from _R. J. Mathar_, Jun 08 2008