A355972 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).

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

Offset

1,1

Links

Table of n, a(n) for n=1..96.

Formula

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.

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 cross-ratios.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A355971 (numerators).

Cf. A000040.

Sequence in context: A099873 A185353 A345712 * A168202 A153455 A193019

Adjacent sequences: A355969 A355970 A355971 * A355973 A355974 A355975

Keyword

nonn,frac

Author

Samir Fridhi, Jul 21 2022

Status

approved