A078432 Number of permutations p of 1,2,...,n such that the denominator of the continued fraction [p(1); p(2),...,p(n)] is prime.

0, 1, 4, 14, 32, 204, 994, 7526, 48636, 421392, 4018976, 41304726, 490878388

Offset

1,3

Links

Table of n, a(n) for n=1..13.

Mathematica

Table[Length@Select[Permutations@Range@n, PrimeQ@Denominator@FromContinuedFraction@#&], {n, 9}] (* Giorgos Kalogeropoulos, Sep 22 2021 *)

Prog

(Python)
from itertools import permutations
from sympy import isprime
from sympy.ntheory.continued_fraction import continued_fraction_reduce
def A078432(n): return sum(1 for p in permutations(range(1, n+1)) if isprime(continued_fraction_reduce(p).q)) # Chai Wah Wu, Sep 22 2021

Crossrefs

Cf. A078431, A078433.

Sequence in context: A323723 A324042 A099590 * A124786 A322009 A228272

Adjacent sequences: A078429 A078430 A078431 * A078433 A078434 A078435

Keyword

nonn,more

Author

Reiner Martin, Dec 30 2002

Extensions

a(10)-a(13) from Robert Gerbicz, Nov 27 2010

Status

approved