

A297005


Values of n for which pi_{3,2}(p_n)  pi_{3,1}(p_n) = 1, where p_n is the nth prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).


3



23338590792, 23338590794, 23338590796, 23338590798, 23338590800, 23338590802, 23338590804, 23338590810, 23338590814, 23338590816, 23338590818, 23338590832, 23338591016, 23338591018, 23338591028, 23338591030, 23338591032, 23338591084, 23338591086, 23338591088, 23338591302, 23338591340, 23338591342, 23338591344, 23338591346, 23338591348, 23338591350, 23338591656, 23338591658, 23338591662
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OFFSET

1,1


COMMENTS

This sequence is a companion sequence to A297006. Starting from a(20591)=216415270060 the sequence includes the second signchanging zone predicted by C. Bays et al. in 2001. The sequence with the first two signchanging zones up to 10^13 contains 84323 terms with a(84323)=216682882512 as its last term (see bfile). In addition, a(1) = A096630(1).


LINKS

Sergei D. Shchebetov, Table of n, a(n) for n = 1..84323
A. Alahmadi, M. Planat, P. SolĂ©, Chebyshev's bias and generalized Riemann hypothesis, HAL Id: hal00650320.
C. Bays and R. H. Hudson, Details of the first region of integers x with pi_{3,2} (x) < pi_{3,1}(x), Math. Comp. 32 (1978), 571576.
C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, Zeros of Dirichlet Lfunctions near the real axis and Chebyshev's bias, J. Number Theory 87 (2001), pp. 5476.
M. DelĂ©glise, P. Dusart, X. Roblot, Counting Primes in Residue Classes, Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp. 15651575.
A. Granville, G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 133.
M. Rubinstein, P. Sarnak, Chebyshev's bias, Experimental Mathematics, Volume 3, Issue 3, 1994, pp. 173197.
Eric Weisstein's World of Mathematics, Prime Quadratic Effect.


CROSSREFS

Cf. A007352, A096629, A096630, A096449, A098044.
Sequence in context: A121841 A306503 A096630 * A233841 A015399 A129475
Adjacent sequences: A297002 A297003 A297004 * A297006 A297007 A297008


KEYWORD

nonn


AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 23 2017


STATUS

approved



