A285851 Denominator of the ratio of alternate consecutive prime gaps: Denominator((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 3, 1, 1, 3, 2, 1, 1, 1, 3, 4, 1, 1, 1, 1, 1, 7, 2, 3, 1, 5, 1, 3, 1, 2, 3, 3, 1, 5, 1, 1, 1, 3, 6, 1, 1, 2, 3, 1, 5, 1, 3, 1, 1, 3, 2, 1, 5, 7, 1, 1, 2, 7, 3, 5, 1, 1, 1, 4, 3, 1, 1, 3, 1, 2, 4, 1, 1, 5, 1, 1, 1, 3, 4, 1, 1, 1, 3, 1, 1, 4, 1, 3, 2, 1, 9, 1, 5, 3, 1, 1, 1, 5

Offset

1,8

Links

Table of n, a(n) for n=1..106.

Formula

a(n) = denominator((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}(A286634(j)/a(j))^((1+(-1)^j)/2) + ((1-(-1)^k)/2)*Product_{j=1..k}(A286634(j)/a(j))^((1-(-1)^j)/2)), for n>0.

A001223(n+2) = (1+(-1)^n)*Product_{j=1..n}(A286634(j)/a(j))^((1+(-1)^j)/2) - ((-1+(-1)^n)/2)*Product_{j=1..n}(A286634(j)/a(j))^((1-(-1)^j)/2), for n>0.

Mathematica

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

Crossrefs

Cf. A286634 (numerators), A001223, A000040, A274225, A276309.

Sequence in context: A214123 A369188 A007862 * A055169 A205131 A175892

Adjacent sequences: A285848 A285849 A285850 * A285852 A285853 A285854

Keyword

nonn,frac

Author

Andres Cicuttin, Apr 27 2017

Status

approved