|
|
A239740
|
|
a(n) = gcd(Sum_{k=1...n} F(k), Product{j=1...n} F(j)), where F(k) is the k-th Fibonacci number.
|
|
2
|
|
|
1, 1, 2, 1, 6, 20, 3, 18, 8, 143, 8, 8, 21, 986, 84, 63, 220, 6764, 55, 770, 144, 46367, 144, 432, 377, 317810, 16588, 377, 43428, 2178308, 987, 53298, 2584, 14930351, 2584, 18088, 6765, 102334154, 784740, 20295, 2054476, 701408732, 17711, 1664834, 46368
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
The Fibonacci numbers in the sequence are 1, 2, 3, 8, 21, 55, 144, 377, 987, ... and a majority are elements of A001906 (F(2*n)= bisection of Fibonacci sequence).
We find consecutive values such that (1, 2), (2, 3), (20, 21), (986, 987), (6764, 6765), (46367, 46368), (317810, 317811), (14930351, 14930352), ...
|
|
LINKS
|
|
|
EXAMPLE
|
The first 8 Fibonacci numbers are 1,1,2,3,5,8,13,21 and 1+1+2+3+5+8+13+21 = 54. So a(8) = gcd(54, 1*1*2*3*5*8*13*21) = 18.
|
|
MAPLE
|
with(combinat, fibonacci):seq(gcd(add(fibonacci(i), i=1..n), mul(fibonacci(j), j=1..n)), n=1..60);
|
|
MATHEMATICA
|
nn=60; With[{prs=Fibonacci[Range[nn]]}, Table[GCD[Total[Take[prs, n]], Times@@Take[ prs, n]], {n, nn}]]
|
|
PROG
|
(Haskell)
a239740 n = gcd (sum fs) (product fs)
where fs = take n $ tail a000045_list
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|