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A274828 Integer part of the alternating n-th 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 (list; graph; refs; listen; history; text; internal format)
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 * A257474 A257317 A163376

Adjacent sequences:  A274825 A274826 A274827 * A274829 A274830 A274831

KEYWORD

sign

AUTHOR

Andres Cicuttin, Jul 07 2016

STATUS

approved

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Last modified December 3 11:37 EST 2020. Contains 338900 sequences. (Running on oeis4.)