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 A136341 Fibonacci primes or semiprimes F(k) such that F(k+1) is again prime or semiprime. 1
 2, 3, 13, 21, 34, 55, 233, 17711 (list; graph; refs; listen; history; text; internal format)
 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 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. 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. [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

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)