A274828 Integer part of the alternating n-th partial sum of the reciprocals of the successive prime gaps.

1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset

1,41

Comments

The graph of the first 15*10^3 terms looks like a realization of a random walk. It has an estimated fractal dimension of about 1.48 (with box counting method) which is closed to that of the random walk (3/2).

Links

Andres Cicuttin, Table of n, a(n) for n = 1..15000

Formula

a(n) = floor(Sum_{i=1..n} ((-1)^(i - 1))/(prime(i+1)-prime(i))).

a(n) = floor(Sum_{i=1..n} ((-1)^(i - 1))/A001223(i)).

Example

The prime gaps (A001223) are 1, 2, 2, 4, 2, 4, 2, .... For n=7, the 7th partial sum is 1/1 - 1/2 + 1/2 - 1/4 + 1/2 - 1/4 + 1/2 = 3/2 so a(7) is the integer part of 3/2, which is 1. - Michael B. Porter, Jul 11 2016

Mathematica

Table[Floor@Sum[((-1)^(j - 1))/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, 100}];

Prog

(PARI) a(n) = floor(sum(i=1, n, ((-1)^(i-1))/(prime(i+1)-prime(i)))) \\ Felix Fröhlich, Jul 07 2016

Crossrefs

Cf. A001223, A217538.

Sequence in context: A043543 A237684 A130634 * A364136 A257474 A257317

Adjacent sequences: A274825 A274826 A274827 * A274829 A274830 A274831

Keyword

sign

Author

Andres Cicuttin, Jul 07 2016

Status

approved