login
Where the prime race 3k-1 vs. 3k+1 changes leader.
(Formerly M2191)
18

%I M2191 #47 Jun 07 2023 08:44:47

%S 2,608981813029,608981813507,608981813683,608981813819,608981814127,

%T 608981814143,608981818999,608981820977,608981826877,608981826977,

%U 608981827873,608981828201,608981836363,608981836493,608981836681

%N Where the prime race 3k-1 vs. 3k+1 changes leader.

%C Terms a(2n+1) form a subsequence of A098044.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence, although the terms are incorrect - see A185703).

%H Donovan Johnson, <a href="/A007352/b007352.txt">Table of n, a(n) for n = 1..39215</a>

%H C. Bays and R. H. Hudson, <a href="http://dx.doi.org/10.1090/S0025-5718-1978-0476616-X">Details of the first region of integers x with pi_{3,2}(x) < pi_{3,1}(x)</a>, Math. Comp. 32 (1978), 571-576.

%H A. Granville and G. Martin, <a href="http://www.jstor.org/stable/27641834">Prime number races</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.

%H G. Martin, <a href="http://arxiv.org/abs/math/0010086">Asymmetries in the Shanks-Renyi Prime number race</a>, arXiv:math/0010086 [math.NT], 2000.

%H Pieter Moree, <a href="https://doi.org/10.1090/S0025-5718-03-01536-9">Chebyshev's bias for composite numbers with restricted prime divisors</a>, Mathematics of computation 73.245 (2004): 425-449. See page 425.

%H M. Rubinstein and P. Sarnak, <a href="http://projecteuclid.org/euclid.em/1048515870">Chebyshev's Bias</a>, Exper. Math. 3 (4) (1994) 209.

%H Robert G. Wilson v, <a href="/A005596/a005596.pdf">Letter to N. J. A. Sloane, Aug. 1993</a>

%Y Cf. A007352, A007350, A007353, A007354, A297406, A297407, A297408, A297410, A297411.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_, Apr 28 1994

%E Terms from a(3) onwards corrected by _Max Alekseyev_, Feb 10 2011