A078433 - OEIS

A078433

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

0, 2, 2, 10, 30, 124, 992, 5700, 39844, 366172, 3587856, 38861778, 435816838

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OFFSET

1,2

LINKS

MATHEMATICA

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

PROG

(PARI) a(n)=sum(i=1, n!, isprime(contfracpnqn(numtoperm(n, i))[1, 1]))

(Python)

from itertools import permutations

from sympy import isprime

from sympy.ntheory.continued_fraction import continued_fraction_reduce

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

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

a(10)-a(11) from Robert Gerbicz, Nov 21 2010

a(12)-a(13) from Robert Gerbicz, Nov 27 2010

STATUS

approved