A099954 Numbers k such that Fibonacci(k) and its reversal are two distinct semiprimes.

19, 22, 31, 41, 59, 107, 193, 199, 227, 467

Offset: 1

Author

Jonathan Vos Post and G. L. Honaker, Jr., Nov 13 2004

Keywords

• nonn
• base
• more

Comments

a(11) > 1000. - Donovan Johnson, Jun 06 2009

a(11) >= 1801. Inclusion of 1801 depends on the factorization of Fibonacci(1801), a 377-digit composite number. - Tyler Busby, Jan 14 2023

Examples

			F(19) = 4181 = 37 * 113, reverse(F(19)) = 1814 = 2 * 907.
		

Links

• factordb, Status of Fibonacci(1801).

Crossrefs

F(a(n)) is the intersection of A053409 and A097393

Programs

Maple

with(combinat): with(numtheory): rev:=proc(n) local nn: nn:=convert(n,base,10): add(nn[nops(nn)+1-j]*10^(j-1),j=1..nops(nn)) end: a:=proc(n): if rev(fibonacci(n))<>fibonacci(n) and bigomega(fibonacci(n))=2 and bigomega(rev(fibonacci(n)))=2 then n else fi end: seq(a(n),n=1..200); # Emeric Deutsch, Jul 26 2006

Mathematica

fspQ[n_]:=Module[{f=Fibonacci[n]},f!=IntegerReverse[f]&&PrimeOmega[f] == PrimeOmega[IntegerReverse[f]]==2]; Select[Range[470],fspQ] (* Harvey P. Dale, Jul 24 2016 *)

PARI

is(k) = {(fib=fibonacci(k))!=(fibrev=fromdigits(Vecrev(digits(fib)))) && (bigomega(fib)==2 && bigomega(fibrev)==2)} \\ Tyler Busby, Jan 07 2023

Extensions

More terms from Emeric Deutsch, Jul 26 2006

a(10) from Donovan Johnson, Jun 06 2009