A226842 Minimum integers equal to (sum_{i=n..n+k} F(i)) / (F(n) - 1), where F(i) are Fibonacci numbers (A000045).

1, 1, 2, 86, 132, 208, 40795, 2247, 88394795, 3595, 1327851384353, 84947964454760903, 137308938406976063, 312435619847, 97479304649455554938376, 23734336322729, 474623017718162543599953606266, 263154851567816, 15843080965993404582885796005881401739

Offset

1,3

Comments

See A226841 for minimum values of k.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..50

Example

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.

Maple

with(numtheory); with(combinat); ListA226842:= proc(q)
local n, a, b, k, p; a:=0;
for n from 1 to q do a:=a+fibonacci(n); b:=fibonacci(n+1); k:=1;
  while not type(b/a, integer) do k:=k+1; b:=b+fibonacci(n+k); od; print(b/a); od; end: ListA226842(10^3);

Crossrefs

Cf. A000045, A000071.

Sequence in context: A101578 A041881 A076542 * A303892 A305284 A304897

Adjacent sequences: A226839 A226840 A226841 * A226843 A226844 A226845

Keyword

nonn

Author

Paolo P. Lava, Jun 19 2013

Status

approved