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%I #17 Oct 30 2022 18:19:59
%S 0,2,2,10,30,124,992,5700,39844,366172,3587856,38861778,435816838
%N Number of permutations p of 1,2,...,n such that the numerator of the continued fraction [p(1); p(2),...,p(n)] is prime.
%t Table[Length@Select[Permutations@Range@n,PrimeQ@Numerator@FromContinuedFraction@#&],{n,9}] (* _Giorgos Kalogeropoulos_, Sep 22 2021 *)
%o (PARI) a(n)=sum(i=1,n!,isprime(contfracpnqn(numtoperm(n,i))[1,1]))
%o (Python)
%o from itertools import permutations
%o from sympy import isprime
%o from sympy.ntheory.continued_fraction import continued_fraction_reduce
%o def A078433(n): return sum(1 for p in permutations(range(1,n+1)) if isprime(continued_fraction_reduce(p).p)) # _Chai Wah Wu_, Sep 22 2021
%Y Cf. A078431, A078432.
%K nonn,more
%O 1,2
%A _Reiner Martin_, Dec 30 2002
%E a(10)-a(11) from _Robert Gerbicz_, Nov 21 2010
%E a(12)-a(13) from _Robert Gerbicz_, Nov 27 2010
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