A361723 Numbers k such that there are 18 primes between 100*k and 100*k + 99.

1228537713709, 23352869714018, 28703237474266, 144785865481702, 161394923966449, 168975708209638, 174748809066898, 207552241231357, 278215179205531, 312303328909720, 592248982143877, 812939886634531, 939100782752014, 983930290209021, 1111161494544274

Offset: 1

Author

Brian Kehrig, Mar 21 2023

Keywords

• nonn

Comments

There are A261571(18) = 948729 possible patterns for centuries having 18 primes.

Examples

			1228537713709 is in the sequence because there are 18 primes between 122853771370900 and 122853771370999: 122853771370900 + x, where x is one of (1, 3, 7, 19, 21, 27, 31, 33, 37, 49, 51, 61, 69, 73, 87, 91, 97, or 99).
		

Links

• Brian Kehrig, Table of n, a(n) for n = 1..39 (terms up to 10^16)
• Note (Apr 24 2024): An older version of the b-file missed a(33) and a(38). The present b-file is correct.

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).

Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes).

Cf. A261571 (number of patterns for centuries with n primes).

Programs

PARI

isok(k) = sum(i=0, 99, isprime(100*k + i)) == 18; \\ Michel Marcus, Mar 23 2023