

A274828


Integer part of the alternating nth partial sum of the reciprocals of the successive prime gaps.


4



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
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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)^(i1))/(prime(i+1)prime(i)))) \\ Felix FrÃ¶hlich, Jul 07 2016


CROSSREFS

Cf. A001223, A217538.
Sequence in context: A043543 A237684 A130634 * A257474 A257317 A163376
Adjacent sequences: A274825 A274826 A274827 * A274829 A274830 A274831


KEYWORD

sign


AUTHOR

Andres Cicuttin, Jul 07 2016


STATUS

approved



