

A355972


Denominator of the crossratio of the four primes p_n, p_{n+1}, p_{n+2}, p_{n+3}, where p_n = prime(n).


1



5, 2, 8, 5, 8, 5, 4, 9, 7, 9, 4, 5, 4, 4, 7, 7, 9, 4, 1, 9, 16, 27, 6, 7, 5, 8, 5, 20, 77, 8, 9, 3, 35, 3, 7, 4, 16, 4, 7, 3, 35, 4, 8, 3, 13, 7, 3, 5, 4, 9, 3, 15, 11, 3, 7, 7, 9, 4, 4, 65, 49, 20, 5, 20, 14, 9, 15, 4, 4, 27, 40, 5, 4, 16, 27, 6, 5, 22, 25, 11, 35, 3, 9, 16, 27, 6, 7, 5, 3, 9, 4, 5, 8, 3, 11, 20
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OFFSET

1,1


LINKS



FORMULA

a(n) = denominator of ((p_np_(n+2))/(p_np_(n+3))) * ((p_(n+1)p_(n+3))/(p_(n+1)p_(n+2))) where p_n = prime(n) is the nth prime.


EXAMPLE

6/5, 3/2, 9/8, 9/5, 9/8, 9/5, 5/4, 10/9, 16/7, 10/9 are the first ten terms in the sequence of crossratios.


MATHEMATICA

dcr[{a_, b_, c_, d_}]:=Denominator[(ac)/(ad) (bd)/(bc)]; dcr/@Partition[Prime[ Range[ 100]], 4, 1] (* Harvey P. Dale, Nov 26 2022 *)


PROG

(PARI) a(n) = my(p=prime(n), p1=nextprime(p+1), p2=nextprime(p1+1), p3=nextprime(p2+1)); denominator((((pp2)/(pp3))*((p1p3)/(p1p2)))); \\ Michel Marcus, Jul 29 2022


CROSSREFS



KEYWORD

nonn,frac


AUTHOR



STATUS

approved



