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

Author

Carlos Eduardo Olivieri, Dec 16 2014

Keywords

• nonn
• easy

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

Examples

			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.
		

Links

• N. MacKinnon and S. M. Gagola, Jr., Fibonacci twin primes (solution to problem 10844), American Mathematical Monthly 109, No. 1 (Jan., 2002), 78.

Crossrefs

Cf. A180422, A000045.

Programs

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]] &]

PARI

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