A175551 Decimal form of the period of 1/Fibonacci(n) for n such that gcd(10,Fibonacci(n)) = 1.

3, 76923, 47619, 1123595505617977528089887640449438202247191

Offset: 1

Author

Michel Lagneau, Jun 26 2010

Keywords

• nonn
• base

Comments

A curiosity: the first six digits (with the first digit zero) of the 4th number, {0,1,1,2,3,5}, are the first six Fibonacci numbers!

The next number of this sequence contains 230 digits (decimal form of the period of 1/233 = 0.004291845493562231759656652360515021459227...).

Examples

			3 is in the sequence because Fibonacci(4) = 3 and 1/3 = 0.3333 => 3;
76923 is in the sequence because Fibonacci(7) = 13, and 1/13 = 0.076923 076923 => 76923.
		

Crossrefs

Cf. A000045, A175545, A178505, A045572, A002329.

Programs

Maple

with(combinat, fibonacci):Digits:=100:nn:=10000:for m from 1 to nn do:n:=fibonacci(m):l:=length(n):z:=evalf(1/n): indic:=0:for p from 1 to nn do:if irem(10^p, n) = 1 and gcd(n, 5) = 1 and indic=0 then pp:=p:indic:=1:z1:=floor(z*10^pp): else fi:od:if indic=1 then printf(`%d, `, z1):else fi:od:

Extensions

Name corrected by T. D. Noe, Jul 06 2010