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A274225 Denominator of the ratio of consecutive prime gaps. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A308916 A182628 A331366 * A028334 A083269 A097306

Adjacent sequences:  A274222 A274223 A274224 * A274226 A274227 A274228

KEYWORD

nonn,frac

AUTHOR

Andres Cicuttin, Jun 19 2016

STATUS

approved

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Last modified August 3 04:47 EDT 2021. Contains 346435 sequences. (Running on oeis4.)