

A136341


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


1




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. [From 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. [From R. J. Mathar, Jun 02 2010]


LINKS

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


FORMULA

Let F(n) = nth Fibonacci number and define a 2almost 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 2almost prime and 89 is prime.


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( k1 ))>2 & next; print1(fibonacci(k)", ")) \\  M. F. Hasler, May 01 2008


CROSSREFS

Cf. A001358.
Cf. A053409, A005478. [From 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

more,nonn


AUTHOR

Cino Hilliard, Mar 28 2008


EXTENSIONS

Edited by M. F. Hasler, May 01 2008


STATUS

approved



