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%I #41 Nov 26 2022 15:51:12
%S 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,
%T 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,
%U 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
%N Denominator of the cross-ratio of the four primes p_n, p_{n+1}, p_{n+2}, p_{n+3}, where p_n = prime(n).
%F a(n) = denominator of ((p_n-p_(n+2))/(p_n-p_(n+3))) * ((p_(n+1)-p_(n+3))/(p_(n+1)-p_(n+2))) where p_n = prime(n) is the n-th prime.
%e 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 cross-ratios.
%t dcr[{a_,b_,c_,d_}]:=Denominator[(a-c)/(a-d) (b-d)/(b-c)]; dcr/@Partition[Prime[ Range[ 100]],4,1] (* _Harvey P. Dale_, Nov 26 2022 *)
%o (PARI) a(n) = my(p=prime(n), p1=nextprime(p+1), p2=nextprime(p1+1), p3=nextprime(p2+1)); denominator((((p-p2)/(p-p3))*((p1-p3)/(p1-p2)))); \\ _Michel Marcus_, Jul 29 2022
%Y Cf. A355971 (numerators).
%Y Cf. A000040.
%K nonn,frac
%O 1,1
%A _Samir Fridhi_, Jul 21 2022
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