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

Offset: 1

Author

N. J. A. Sloane, Feb 20 2018

Keywords

• nonn

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

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

Crossrefs

Cf. A065358, A064940.

Programs

Mathematica

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

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
    if 0 < k <= pn:
        A299300_list.append(n+k)
    d += -pn if r else pn
    r, n, p = not r, p, nextprime(p) # Chai Wah Wu, Feb 21 2018