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A226842 Minimum integers equal to (sum_{i=n..n+k} F(i)) / (F(n) - 1), where F(i) are Fibonacci numbers (A000045). 2
1, 1, 2, 86, 132, 208, 40795, 2247, 88394795, 3595, 1327851384353, 84947964454760903, 137308938406976063, 312435619847, 97479304649455554938376, 23734336322729, 474623017718162543599953606266, 263154851567816, 15843080965993404582885796005881401739 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 7 14:13 EDT 2022. Contains 357271 sequences. (Running on oeis4.)