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

1,1

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

Links

Table of n, a(n) for n=1..10.

factordb, Status of Fibonacci(1801).

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A113868 A056025 A284670 * A335347 A374465 A050955

Adjacent sequences: A099951 A099952 A099953 * A099955 A099956 A099957

Keyword

nonn,base,more

Author

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

Extensions

More terms from Emeric Deutsch, Jul 26 2006

a(10) from Donovan Johnson, Jun 06 2009

Status

approved