login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A113188 Primes that are the difference of two Fibonacci numbers; primes in A007298. 12
2, 3, 5, 7, 11, 13, 19, 29, 31, 47, 53, 89, 131, 139, 199, 233, 521, 607, 953, 1453, 1597, 2207, 2351, 2579, 3571, 6763, 9349, 10891, 28513, 28649, 28657, 42187, 44771, 46279, 75017, 189653, 317777, 514229, 1981891, 2177699, 3010349, 3206767 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The difference F(i)-F(j) equals the sum F(j-1)+...+F(i-2) [Corrected by Patrick Capelle, Mar 01 2008]. In general, we need gcd(i,j)=1 for F(i)-F(j) to be prime. The exceptions are handled by the following rule: if i and j are both even or both odd, then F(i)-F(j) is prime if either (1) i-j=4 and L(i-2) is a Lucas prime or (2) i-j=2 and F(i-1) is a Fibonacci prime.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

EXAMPLE

The prime 139 is here because it is F(12)-F(5).

MATHEMATICA

lst={}; Do[p=Fibonacci[n]-Fibonacci[i]; If[PrimeQ[p], AppendTo[lst, p]], {n, 2, 40}, {i, n-1}]; Union[lst]

PROG

(PARI) list(lim)=my(v=List(), F=vector(A130233(lim), i, fibonacci(i)), s, t); for(i=1, #F, s=0; forstep(j=i, 1, -1, s+=F[j]; if(s>lim, break); if(isprime(s), listput(v, s)))); Set(v) \\ Charles R Greathouse IV, Oct 07 2016

CROSSREFS

Cf. A000045 (Fibonacci numbers), A001605 (Fibonacci(n) is prime), A001606 (Lucas(n) is prime), A113189 (number of times that Fibonacci(n)-Fibonacci(i) is prime for i=0..n-3).

Sequence in context: A114111 A155108 A222565 * A242738 A079153 A020616

Adjacent sequences:  A113185 A113186 A113187 * A113189 A113190 A113191

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 17 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 25 11:59 EDT 2017. Contains 288710 sequences.