A175026 Fibonacci entry points: a(n) = smallest m such that prime(A075702(n)) divides Fibonacci(m).

432, 127, 1426, 10488, 63221, 1328, 11136, 1291186

Offset

1,1

Comments

In all cases, a(n) is one of divisors of (A075702(n)):

{2160,3048,27094,251712,505768,936240,2182656,2582372}/

{432,127,1426,10488,63221,1328,11136,1291186} = {5,24,19,24,8,705,196,2}.

This is used in Mathematica code for faster search.

Links

Table of n, a(n) for n=1..8.

Formula

a(n)=A001602(A075702(n)).

Example

a(1)=432 because A075702(1)=2160=5*432, prime(2160)=19009, and F(432)/19009= 45104130506533126693784341438185160821786395872599778181861900641867287643757057395776.

Mathematica

s={2160, 3048, 27094, 251712, 505768, 936240, 2182656, 2582372};
Do[sk=s[[k]]; dv=Divisors[sk]; i=2; While[Mod[Fibonacci[dvi=dv[[i]]], Prime[sk]]>0, i++ ]; Print[dvi], {k, 8}]

Crossrefs

Cf. A001177, A001602, A075702.

Sequence in context: A048961 A301645 A063463 * A205192 A066419 A245469

Adjacent sequences: A175023 A175024 A175025 * A175027 A175028 A175029

Keyword

nonn

Author

Zak Seidov, Nov 03 2009

Status

approved