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%I #14 Jun 20 2013 14:43:45
%S 1,1,2,86,132,208,40795,2247,88394795,3595,1327851384353,
%T 84947964454760903,137308938406976063,312435619847,
%U 97479304649455554938376,23734336322729,474623017718162543599953606266,263154851567816,15843080965993404582885796005881401739
%N Minimum integers equal to (sum_{i=n..n+k} F(i)) / (F(n) - 1), where F(i) are Fibonacci numbers (A000045).
%C See A226841 for minimum values of k.
%H Paolo P. Lava, <a href="/A226842/b226842.txt">Table of n, a(n) for n = 1..50</a>
%e The sum of first 10 Fibonacci numbers is 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 = 143. We need to add at least 17 consecutive Fibonacci numbers, starting from F(11)=89, in order to have 89 + 144 + 233 + 377 + 610 + 987 + 1597 + 2584 + 4181 + 6765 + 10946 + 17711 + 28657 + 46368 + 75025 + 121393 + 196418 = 514085 and 514085 / 143 = 3595. Hence a(10) = 3595.
%p with(numtheory); with(combinat); ListA226842:= proc(q)
%p local n,a,b,k,p; a:=0;
%p for n from 1 to q do a:=a+fibonacci(n); b:=fibonacci(n+1); k:=1;
%p while not type(b/a,integer) do k:=k+1; b:=b+fibonacci(n+k); od; print(b/a); od; end: ListA226842(10^3);
%Y Cf. A000045, A000071.
%K nonn
%O 1,3
%A _Paolo P. Lava_, Jun 19 2013
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