A299300 - OEIS

A299300

Values of k such that A065358(k-1) = 0.

1, 3, 7, 35, 39, 43, 51, 55, 79, 87, 91, 107, 111, 115, 835, 843, 1391, 1407, 1411, 1471, 1579, 1587, 1651, 1663, 1843, 1851, 3383, 3491, 3507, 3515, 3519, 3547, 3659, 3691, 3719, 3747, 3779, 3819, 3823, 3843, 3851, 3855, 3871, 3899, 3939, 3947, 3987, 3991

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OFFSET

1,2

COMMENTS

Obtained by adding 1 to the terms of A064940.

Fraile et al. (2017) describe essentially the same sequence as A065358 except with offset 1 instead of 0. So the present sequence gives the values of k so that their version of the Jacob's Ladder sequence has the value 0.

For the first 7730 terms, see the b-file in A064940.

LINKS

Table of n, a(n) for n=1..48.

Alberto Fraile, Roberto Martínez, and Daniel Fernández, Jacob's Ladder: Prime numbers in 2d, arXiv preprint arXiv:1801.01540 [math.HO], 2017.

MATHEMATICA

A065358:= Table[Sum[(-1)^(PrimePi[k]), {k, 1, n}], {n, 0, 500}]; Select[Range[50], A065358[[#]] == 0 &] (* G. C. Greubel, Feb 20 2018 *)

PROG

(Python)

from sympy import nextprime

A299300_list, p, d, n, r = [], 2, -1, 0, False

while n <= 10**6:

pn, k = p-n, d if r else -d