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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117517 Numbers n such that F(2*n + 1) is prime where F(m) is the Fibonacci number. 1
1, 2, 3, 5, 6, 8, 11, 14, 21, 23, 41, 65, 68, 179, 215, 216, 224, 254, 284, 285, 1485, 2361, 2693, 4655, 4838, 7215, 12780, 15378, 17999, 18755, 25416, 40919, 52455, 65010, 74045, 100553, 198689, 216890, 295020, 296844, 302355, 465758, 524948, 642803, 818003, 901529, 984360, 1452176 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For F(n) to be prime, with n>4, it is necessary but not sufficient for n to be prime. Hence after F(4) = 3, every prime F(m) is of the form F(2*n+1) for some n. Every prime divides some Fibonacci number. See also comment to A093062. - Jonathan Vos Post, Apr 29 2006

LINKS

Table of n, a(n) for n=1..48.

H. Dubner and W. Keller, New Fibonacci and Lucas Primes, Math. Comp. 68 (1999) 417-427.

FORMULA

a(n) = (A083668(n)-1)/2. - R. J. Mathar, Jul 08 2009

a(n) = (A001605(n+1)-1)/2, n>1. - Vincenzo Librandi, May 24 2016

EXAMPLE

If n=68 then F(2*n + 1) is a prime with twenty nine digits.

MATHEMATICA

Select[Range[0, 5000], PrimeQ[Fibonacci[2 # + 1]] &] (* Vincenzo Librandi, May 24 2016 *)

PROG

(MAGMA) [n: n in [0..1000] | IsPrime(Fibonacci(2*n+1))]; // Vincenzo Librandi, May 24 2016

CROSSREFS

Cf. A000045, A001605, A117595.

Cf. A001602, A022307, A030427, A051694, A075737, A083668, A099000.

Sequence in context: A127312 A081830 A238006 * A098491 A280449 A107947

Adjacent sequences:  A117514 A117515 A117516 * A117518 A117519 A117520

KEYWORD

nonn

AUTHOR

Parthasarathy Nambi, Apr 26 2006

EXTENSIONS

More terms from Vincenzo Librandi, May 24 2016

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 16:46 EDT 2019. Contains 328373 sequences. (Running on oeis4.)