A298821 Primes p for which pi_{24,19}(p) - pi_{24,1}(p) = -1, where pi_{m,a}(x) is the number of primes <= x which are congruent to a (mod m).

706866045116113, 706866045126361, 706866045126697, 706866045126907, 706866045128377, 706866045128563, 706866045128953, 706866045129163, 706866045129403, 706866045130057, 706866045130153, 706866045130459, 706866045130723, 706866045130771, 706866045131107, 706866045155113, 706866045155899, 706866045156043, 706866045156409, 706866045156499

Offset

1,1

Comments

This is a companion sequence to A298820 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) = 766164822666883 as the last one.

Links

Andrey S. Shchebetov and 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: A338608 A088867 A256234 * A159042 A129935 A173405

Adjacent sequences: A298818 A298819 A298820 * A298822 A298823 A298824

Keyword

nonn

Author

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

Status

approved