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

1,4

Links

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

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)

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A182628 A361477 A331366 * A028334 A083269 A097306

Adjacent sequences: A274222 A274223 A274224 * A274226 A274227 A274228

Keyword

nonn,frac

Author

Andres Cicuttin, Jun 19 2016

Status

approved