A136341 Fibonacci primes or semiprimes F(k) such that F(k+1) is again prime or semiprime.

2, 3, 13, 21, 34, 55, 233, 17711

Offset

1,1

Comments

By definition, the smaller number in a pair of two consecutive Fibonacci numbers in A061305. a(9), if it exists, is >= A000045(230), so it has at least 48 digits. [R. J. Mathar, Feb 06 2010]

A search for consecutive numbers in the union of A072381 and A001605 shows that a(9) must be larger than A000045(990), a number with 207 digits, if it exists. [R. J. Mathar, Jun 02 2010]

Links

Table of n, a(n) for n=1..8.

Formula

Let F(n) = n-th Fibonacci number and define a 2-almost prime number to be a number with only 2 prime divisors with multiplicity.

Example

(55,89) is an almost twin Fibonacci prime pair because 55=5*11 is a 2-almost prime and 89 is prime.

Mathematica

Fibonacci[#]&/@(SequencePosition[Table[If[PrimeOmega[f]<=2, 1, 0], {f, Fibonacci[ Range[150]]}], {1, 1}][[All, 1]]) (* Harvey P. Dale, Mar 29 2022 *)

Prog

(PARI) ATfib(n) = for(x=3, n, f1=fibonacci(x); f2=fibonacci(x+1); if(bigomega (f1)<=2&&bigomega(f2)<=2, print1(f1", ")))
(PARI) for( k=3, 10^5, bigomega( fibonacci( k++ ))>2 & next; bigomega( fibonacci( k-1 ))>2 & next; print1(fibonacci(k--)", ")) \\ M. F. Hasler, May 01 2008

Crossrefs

Cf. A001358.

Cf. A053409, A005478. [R. J. Mathar, Jun 02 2010]

Cf. A001605, A072381, A278637.

Sequence in context: A229117 A295722 A037392 * A139563 A019226 A138699

Adjacent sequences: A136338 A136339 A136340 * A136342 A136343 A136344

Keyword

nonn,more

Author

Cino Hilliard, Mar 28 2008

Extensions

Edited by M. F. Hasler, May 01 2008

Status

approved