

A252296


Fibonacci numbers k for which the difference between k and the largest prime less than k is also prime.


0



5, 13, 21, 34, 55, 144, 610, 2584, 6765, 10946, 46368, 196418, 832040, 14930352, 267914296, 1134903170, 4807526976, 365435296162, 1548008755920, 117669030460994, 498454011879264, 2111485077978050, 160500643816367088, 12200160415121876738, 51680708854858323072
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OFFSET

1,1


COMMENTS

a(n)  p = q, where a(n) is a Fibonacci number, p is the largest prime less than a(n), and q is also prime.
The only terms that are primes are 5 and 13, since there are no other Fibonacci numbers that are twin primes: see the MacKinnon and Gagola link.  Robert Israel, Jan 13 2015


LINKS

Table of n, a(n) for n=1..25.
N. MacKinnon and S. M. Gagola, Jr., Fibonacci twin primes (solution to problem 10844), American Mathematical Monthly 109, No. 1 (Jan., 2002), 78.


EXAMPLE

For n = 1: a(1) = 5, 5  3 = 2.
For n = 4: a(4) = 34, 34  31 = 3.
For n = 7: a(7) = 610, 610  607 = 3.
For n = 11: a(11) = 46368, 46368  46351 = 17.


MAPLE

select(t > isprime(t  prevprime(t)), [seq(combinat:fibonacci(n), n=4..1000)]); # Robert Israel, Dec 16 2014


MATHEMATICA

Select[ Fibonacci@ Range[4, 100], PrimeQ[#  NextPrime[#, 1]] &]


PROG

(PARI) for(n=1, 100, f=fibonacci(n); if(f>2&&isprime(fprecprime(f1)), print1(f, ", "))) \\ Derek Orr, Dec 30 2014


CROSSREFS

Cf. A180422, A000045.
Sequence in context: A299770 A294962 A316357 * A273569 A273750 A191116
Adjacent sequences: A252293 A252294 A252295 * A252297 A252298 A252299


KEYWORD

nonn,easy


AUTHOR

Carlos Eduardo Olivieri, Dec 16 2014


STATUS

approved



