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).

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..93.

Formula

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.

Example

Cross-ratio 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((((p-p2)/(p-p3))*((p1-p3)/(p1-p2)))); \\ Michel Marcus, Jul 29 2022

Crossrefs

Cf. A000040, A355972 (denominators).

Sequence in context: A176533 A214497 A177015 * A327000 A249948 A066070

Adjacent sequences: A355968 A355969 A355970 * A355972 A355973 A355974

Keyword

nonn,frac

Author

Samir Fridhi, Jul 21 2022

Status

approved