A252296 Fibonacci numbers k for which the difference between k and the largest prime less than k is also prime.

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

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(f-precprime(f-1)), 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