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A099954
Numbers k such that Fibonacci(k) and its reversal are two distinct semiprimes.
1
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
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
KEYWORD
nonn,base,more
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, Jul 26 2006
a(10) from Donovan Johnson, Jun 06 2009
STATUS
approved