A298820 Values of n for which pi_{24,19}(p_n) - pi_{24,1}(p_n) = -1, where p_n is the n-th prime and pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

21317046795798, 21317046796093, 21317046796102, 21317046796104, 21317046796154, 21317046796159, 21317046796172, 21317046796185, 21317046796193, 21317046796208, 21317046796212, 21317046796221, 21317046796226, 21317046796229, 21317046796240, 21317046796968, 21317046796986, 21317046796992, 21317046797002, 21317046797007

Offset

1,1

Comments

This is a companion sequence to A298821 and the first discovered for pi_{24,19}(p) - pi_{24,1}(p) prime race. The full sequence up to 10^15 contains 5 sign-changing zones with 3436990 terms in total with A(3436990) = 23049274819456 as the last one.

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

Cf. A295355, A295356, A297449, A297450

Sequence in context: A255359 A011527 A172543 * A246110 A015438 A082249

Adjacent sequences: A298817 A298818 A298819 * A298821 A298822 A298823

Keyword

nonn

Author

Andrey S. Shchebetov and Sergei D. Shchebetov, Jan 27 2018

Status

approved