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A355971 Numerator of the cross-ratio of the four primes p_n, p_{n+1}, p_{n+2}, p_{n+3}, where p_n = prime(n). 1

%I #65 Aug 02 2022 09:18:08

%S 6,3,9,9,9,9,5,10,16,10,5,9,5,5,8,16,10,5,2,10,25,35,7,9,9,9,9,27,81,

%T 15,10,8,36,8,8,5,25,5,8,8,36,9,9,7,14,8,4,9,5,10,8,16,16,4,8,16,10,5,

%U 9,72,54,27,9,27,15,16,16,9,5,35,49,7,5,25,35,7,9,27,27,36,36,8,10,25,35,7,9,9,4,10,5,9,9

%N Numerator of the cross-ratio of the four primes p_n, p_{n+1}, p_{n+2}, p_{n+3}, where p_n = prime(n).

%C Conjecture: all integers >= 2 occur at least once among the sequence of cross-ratios.

%F a(n) = numerator 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 Cross-ratio fractions begin 6/5, 3/2, 9/8, 9/5, 9/8, 9/5, 5/4, 10/9, 16/7, 10/9, ...

%o (PARI) a(n) = my(p=prime(n), p1=nextprime(p+1), p2=nextprime(p1+1), p3=nextprime(p2+1)); numerator((((p-p2)/(p-p3))*((p1-p3)/(p1-p2)))); \\ _Michel Marcus_, Jul 29 2022

%Y Cf. A000040, A355972 (denominators).

%K nonn,frac

%O 1,1

%A _Samir Fridhi_, Jul 21 2022

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Last modified April 15 10:24 EDT 2024. Contains 371681 sequences. (Running on oeis4.)