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A274263 Integer part of the ratio of consecutive prime gaps. 9
2, 1, 2, 0, 2, 0, 2, 1, 0, 3, 0, 0, 2, 1, 1, 0, 3, 0, 0, 3, 0, 1, 1, 0, 0, 2, 0, 2, 3, 0, 1, 0, 5, 0, 3, 1, 0, 1, 1, 0, 5, 0, 2, 0, 6, 1, 0, 0, 2, 1, 0, 5, 0, 1, 1, 0, 3, 0, 0, 5, 1, 0, 0, 2, 3, 0, 1, 0, 2, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 0, 5, 0, 3, 0, 1, 1, 0, 0, 2, 3, 0, 0, 2, 0, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It seems that the distribution of the ratios of consecutive prime gaps exhibits a quite symmetric pattern, in the sense that the relative frequency of each ratio is similar to that of the inverse of that ratio (at least for the first 2*10^5 primes). This is more clearly seen by mean of a histogram of the logarithm of the ratios which is nearly symmetric and nearly centered around zero (see link).

Integer part of 2, 1, 2, 1/2, 2, 1/2, 2, 3/2, 1/3, 3, 2/3, 1/2,.... - R. J. Mathar, Jun 26 2016

LINKS

Table of n, a(n) for n=1..96.

Andres Cicuttin, Several histograms of the logarithm of the ratio of consecutive prime gaps (prime(n+2)-prime(n+1))/(prime(n+1)-prime(n)) obtained for the first 2*10^5 primes with different bin sizes

FORMULA

a(n) = floor( A001223(n+1)/A001223(n)).

EXAMPLE

For n = 1 we have (prime(3)-prime(2))/(prime(2)-prime(1))) = (5-3)/(3-2) = 2 and its integer part is 2: a(1) = 2.

For n = 4 we have (prime(6)-prime(5))/(prime(5)-prime(4))) = (13-11)/(11-7) = 1/2 an its integer part is 0: a(4) = 0.

MAPLE

A274264 := proc(n)

    A001223(n+1)/A001223(n) ;

    floor(%) ;

end proc: # R. J. Mathar, Jun 26 2016

MATHEMATICA

Table[Floor[(Prime[j+2]-Prime[j+1])/(Prime[j+1]-Prime[j])], {j, 1, 200}];

IntegerPart[#[[2]]/#[[1]]]&/@Partition[Differences[Prime[Range[200]]], 2, 1] (* Harvey P. Dale, Mar 07 2018 *)

PROG

(PARI) a(n) = (prime(n+2)-prime(n+1))\(prime(n+1)-prime(n)); \\ Michel Marcus, Jun 18 2016

CROSSREFS

Cf. A001223.

Sequence in context: A275768 A117167 A117169 * A046920 A107599 A156836

Adjacent sequences:  A274260 A274261 A274262 * A274264 A274265 A274266

KEYWORD

nonn

AUTHOR

Andres Cicuttin, Jun 17 2016

STATUS

approved

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Last modified March 23 02:58 EDT 2019. Contains 321422 sequences. (Running on oeis4.)