

A355971


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


1



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, 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, 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
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OFFSET

1,1


COMMENTS

Conjecture: all integers >= 2 occur at least once among the sequence of crossratios.


LINKS



FORMULA

a(n) = numerator 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

Crossratio fractions begin 6/5, 3/2, 9/8, 9/5, 9/8, 9/5, 5/4, 10/9, 16/7, 10/9, ...


PROG

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


CROSSREFS



KEYWORD

nonn,frac


AUTHOR



STATUS

approved



