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A272863 Numerator of the ratio of consecutive prime gaps. 5
2, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 1, 3, 2, 1, 3, 2, 3, 4, 1, 1, 2, 1, 2, 7, 2, 3, 1, 5, 1, 3, 1, 2, 3, 1, 1, 5, 1, 2, 1, 6, 1, 1, 1, 2, 3, 1, 5, 3, 1, 1, 1, 3, 2, 1, 5, 7, 2, 1, 2, 7, 3, 5, 1, 2, 3, 4, 3, 1, 2, 3, 4, 1, 2, 5, 1, 5, 1, 3, 2, 3, 4, 1, 1, 2, 3, 2, 1, 2, 1, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

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

A001223(n) = Product_{k=1..n-1} a(k)/A274225(k). - Andres Cicuttin, Apr 26 2017

A000040(n) = 3 + Sum_{j=1..n-1} Product_{k=1..j} a(k)/A274225(k), for n>1. - Andres Cicuttin, Apr 26 2017

MATHEMATICA

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

PROG

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

(PARI) a(n) = numerator((prime(n+2)-prime(n+1))/(prime(n+1)-prime(n))); \\ Michel Marcus, Apr 29 2017

CROSSREFS

Cf. A000040, A001223, A274225 (denominators), A274263.

Cf. A184247 (primes of the form prime(k+1) when a(k)=1).

Sequence in context: A103682 A023134 A304536 * A112632 A254575 A275344

Adjacent sequences:  A272860 A272861 A272862 * A272864 A272865 A272866

KEYWORD

nonn,frac

AUTHOR

Andres Cicuttin, Jun 21 2016

STATUS

approved

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Last modified February 17 17:12 EST 2019. Contains 320222 sequences. (Running on oeis4.)