A285851 -id:A285851 - cp's OEIS frontend

A286634 Numerator of the ratio of alternate consecutive prime gaps: Numerator ((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).

2, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 7, 1, 3, 1, 5, 1, 3, 3, 2, 1, 3, 1, 5, 1, 2, 1, 3, 6, 1, 1, 1, 3, 1, 5, 3, 3, 1, 1, 1, 2, 1, 5, 7, 2, 1, 1, 7, 3, 5, 1, 2, 3, 2, 1, 3, 2, 1, 2, 2, 1, 5, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 6, 2, 1, 1, 1, 3, 3, 1, 3, 3, 5, 1

Offset: 1

Andres Cicuttin, May 11 2017

Cf. A285851 (denominators), A001223, A000040, A272863, A276309.

Table[Numerator[(Prime[k+3]-Prime[k+2])/(Prime[k+1]-Prime[k])], {k, 100}]

a(n) = numerator((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).
A000040(n+3) = 5 + Sum_{k=1..n} ((1+(-1)^k)*Product_{j=1..k}(a(j)/A285851(j))^((1+(-1)^j)/2) + ((1-(-1)^k)/2)*Product_{j=1..k}(a(j)/A285851(j))^((1-(-1)^j)/2)), for n>0.
A001223(n+2) = (1+(-1)^n)*Product_{j=1..n}(a(j)/A285851(j))^((1+(-1)^j)/2) - ((-1+(-1)^n)/2)*Product_{j=1..n}(a(j)/A285851(j))^((1-(-1)^j)/2), for n>0

cp's OEIS Frontend

A286634 Numerator of the ratio of alternate consecutive prime gaps: Numerator ((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).

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