

A297355


Primes p for which pi_{12,5}(p)  pi_{12,1}(p) = 1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).


2



25726067172577, 25726067172857, 25726067173321, 25726067173441, 25726067174389, 25726067174461, 25726067174653, 25726067174761, 25726067175961, 25726067176549, 25726067176669, 25726067176993, 25726067177149, 25726067177429, 25726067177449, 25726067177593, 25726067177617, 25726067177689, 25726067177801, 25726067178013
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OFFSET

1,1


COMMENTS

This is a companion sequence to A297354 and includes the first discovered signchanging zone for pi_{12,5}(p)  pi_{12,1}(p) prime race. The full sequence checked up to 10^14 has 8399 terms (see bfile).


LINKS

Sergei D. Shchebetov, Table of n, a(n) for n = 1..8399
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.
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. A007350, A007351, A038691, A051024, A066520, A096628, A096447, A096448, A199547, A297354.
Sequence in context: A104834 A350363 A289149 * A297357 A080124 A121843
Adjacent sequences: A297352 A297353 A297354 * A297356 A297357 A297358


KEYWORD

nonn


AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 29 2017


STATUS

approved



