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A295356 Primes p for which pi_{24,13}(p) - pi_{24,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m). 6
978412359121, 978412359637, 978412360813, 978412360957, 978412361293, 978412361713, 978412374613, 978412374673, 978412374817, 978412375441, 978412375597, 978412376197, 978412466749, 978412469581, 978412470193, 978412470241, 978412470877, 978412471081, 978412471357, 978412471789 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is a companion sequence to A295355. The sequence (without exact first and last terms as well as the number of terms) was found by Bays and Hudson in 1978 (see references). The full sequence up to 10^15 contains 6 sign-changing zones with 2381904 terms in total with A(2381904) = 699914738212849 as the last one.

We found the 7th sign-changing zone between 10^15 and 10^16. It starts with A(2381905) = 8744052767229817, ends with A(2792591) = 8772206355445549 and contains 410687 terms. - Andrey S. Shchebetov and Sergei D. Shchebetov, Apr 26 2019

LINKS

Sergei D. Shchebetov, Table of n, a(n) for n = 1..100000

A. Granville, G. Martin, Prime Number Races, Amer. Math. Monthly 113 (2006), no. 1, 1-33.

Richard H. Hudson, Carter Bays, The appearance of tens of billion of integers x with pi_{24, 13}(x) < pi_{24, 1}(x) in the vicinity of 10^12, Journal für die reine und angewandte Mathematik, 299/300 (1978), 234-237. MR 57 #12418.

M. Rubinstein, P. Sarnak, Chebyshev’s bias, Experimental Mathematics, Volume 3, Issue 3, 1994, Pages 173-197.

Eric Weisstein's World of Mathematics, Prime Quadratic Effect.

CROSSREFS

Sequence in context: A234195 A297356 A172853 * A180616 A017184 A017280

Adjacent sequences:  A295353 A295354 A295355 * A295357 A295358 A295359

KEYWORD

nonn

AUTHOR

Andrey S. Shchebetov and Sergei D. Shchebetov, Dec 22 2017

STATUS

approved

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Last modified October 23 09:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)