A274225 Denominator of the ratio of consecutive prime gaps.

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, 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, 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

Offset: 1

Author

Andres Cicuttin, Jun 19 2016

Keywords

• nonn
• frac

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A001223, A272863 (numerators), A274263.

Programs

Magma

[Denominator((NthPrime(n+2)-NthPrime(n+1))/(NthPrime(n+1)-NthPrime(n))): n in [1..100]]; // Vincenzo Librandi, Apr 27 2017

Mathematica

Table[(Prime[j+2]-Prime[j+1])/(Prime[j+1]-Prime[j]),{j,1,120}]//Denominator

Formula

a(n) = denominator((prime(n+2)-prime(n+1))/(prime(n+1)-prime(n))).

From Andres Cicuttin, Apr 26 2017: (Start)

A001223(n) = Product_{k=1..n-1} A272863(k)/a(k).

A000040(n) = 3 + Sum_{j=1..n-1} Product_{k=1..j} A272863(k)/a(k), for n>1. (End)