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%I #42 Sep 08 2022 08:46:17
%S 1,1,1,2,1,2,1,2,3,1,3,2,1,2,1,3,1,3,2,1,3,2,3,2,2,1,2,1,2,7,2,3,1,5,
%T 1,1,3,2,1,3,1,5,1,2,1,1,3,2,1,2,3,1,5,1,1,3,1,3,2,1,5,7,2,1,2,7,3,5,
%U 1,2,3,4,1,3,2,3,2,1,4,5,1,5,1,3,2,3,2,2,1,1,3,2,1,2,2,1,6,1,3,3,5,1,3,1,3,5,1,3,1,1,3
%N Denominator of the ratio of consecutive prime gaps.
%H Vincenzo Librandi, <a href="/A274225/b274225.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = denominator((prime(n+2)-prime(n+1))/(prime(n+1)-prime(n))).
%F From _Andres Cicuttin_, Apr 26 2017: (Start)
%F A001223(n) = Product_{k=1..n-1} A272863(k)/a(k).
%F A000040(n) = 3 + Sum_{j=1..n-1} Product_{k=1..j} A272863(k)/a(k), for n>1. (End)
%t Table[(Prime[j+2]-Prime[j+1])/(Prime[j+1]-Prime[j]),{j,1,120}]//Denominator
%o (Magma) [Denominator((NthPrime(n+2)-NthPrime(n+1))/(NthPrime(n+1)-NthPrime(n))): n in [1..100]]; // _Vincenzo Librandi_, Apr 27 2017
%Y Cf. A000040, A001223, A272863 (numerators), A274263.
%K nonn,frac
%O 1,4
%A _Andres Cicuttin_, Jun 19 2016
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