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A299300 Values of k such that A065358(k-1) = 0.

%I A299300 #20 Feb 21 2018 19:10:46
%S A299300 1,3,7,35,39,43,51,55,79,87,91,107,111,115,835,843,1391,1407,1411,
%T A299300 1471,1579,1587,1651,1663,1843,1851,3383,3491,3507,3515,3519,3547,
%U A299300 3659,3691,3719,3747,3779,3819,3823,3843,3851,3855,3871,3899,3939,3947,3987,3991
%N A299300 Values of k such that A065358(k-1) = 0.
%C A299300 Obtained by adding 1 to the terms of A064940.
%C A299300 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.
%C A299300 For the first 7730 terms, see the b-file in A064940.
%H A299300 Alberto Fraile, Roberto Martínez, and Daniel Fernández, <a href="https://arxiv.org/abs/1801.01540">Jacob's Ladder: Prime numbers in 2d</a>, arXiv preprint arXiv:1801.01540 [math.HO], 2017.
%t A299300 A065358:= Table[Sum[(-1)^(PrimePi[k]), {k,1,n}], {n, 0, 500}]; Select[Range[50], A065358[[#]] == 0 &] (* _G. C. Greubel_, Feb 20 2018 *)
%o A299300 (Python)
%o A299300 from sympy import nextprime
%o A299300 A299300_list, p, d, n, r = [], 2, -1, 0, False
%o A299300 while n <= 10**6:
%o A299300     pn, k = p-n, d if r else -d
%o A299300     if 0 < k <= pn:
%o A299300         A299300_list.append(n+k)
%o A299300     d += -pn if r else pn
%o A299300     r, n, p = not r, p, nextprime(p) # _Chai Wah Wu_, Feb 21 2018
%Y A299300 Cf. A065358, A064940.
%K A299300 nonn
%O A299300 1,2
%A A299300 _N. J. A. Sloane_, Feb 20 2018