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 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). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 01:45 EST 2023. Contains 367616 sequences. (Running on oeis4.)