A064940 Values of k for which A065358(k) is 0.

0, 2, 6, 34, 38, 42, 50, 54, 78, 86, 90, 106, 110, 114, 834, 842, 1390, 1406, 1410, 1470, 1578, 1586, 1650, 1662, 1842, 1850, 3382, 3490, 3506, 3514, 3518, 3546, 3658, 3690, 3718, 3746, 3778, 3818, 3822, 3842, 3850, 3854, 3870, 3898, 3938, 3946, 3986, 3990

Offset: 1

Author

Jason Earls, Oct 31 2001

Keywords

• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..11631 (first 151 terms from Harry J. Smith)
• Alberto Fraile, Roberto Martínez, and Daniel Fernández, Jacob's Ladder: Prime numbers in 2d, arXiv preprint arXiv:1801.01540 [math.HO], 2017. [They describe essentially the same sequence as A065358 except with offset 1 instead of 0, so their values for this sequence, which are given in A299300, differ by 1. - _N. J. A. Sloane_, Feb 20 2018]
• Hans Havermann, Graph of first 30 million terms of A065358.
• Hans Havermann, A064940 organized by axis crossing. The last number in a line is the axis crosser. Any number preceding it is a bouncer.
• Don Reble, Table of n, a(n) for n = 1..97863 (The last term in the file is a(97863) = 694777169210.)

Crossrefs

Cf. A065357, A299300.

Programs

Maple

m:= -1:
t:= 0:
Res:= 0,2:
for i from 3 to 5*10^7 by 2 do
  if isprime(i) then m:= -m fi;
  t:= t+2*m;
  if t = 0 then Res:= Res, i+1 fi;
od:
Res; # Robert Israel, Feb 20 2018

Mathematica

A065358 := Table[Sum[(-1)^(PrimePi[k]), {k,1,n}], {n,0,500}]; Select[Range[300], A065358[[#]] == 0 &] - 1  (* G. C. Greubel, Feb 20 2018 *)
c = s = 0; k = 1; lst = {0}; While[k < 100000, c = Mod[c + Boole[PrimeQ[k]], 2]; s = s + (-1)^c; If[s == 0, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Feb 20 2018 *)

PARI

{ n=s=0; for (m=1, 10^9, s+=(-1)^primepi(m); if (s==0, write("b064940.txt", n++, " ", m); if (n==150, return)) ) } \\ Harry J. Smith, Sep 30 2009

Python

from sympy import nextprime
A064940_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:
        A064940_list.append(n+k-1)
    d += -pn if r else pn
    r, n, p = not r, p, nextprime(p) # Chai Wah Wu, Feb 21 2018

Extensions

Initial term 0 added by N. J. A. Sloane, Feb 20 2018