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Numbers k such that there are 18 primes between 100*k and 100*k + 99.
20

%I #47 May 19 2024 11:50:21

%S 1228537713709,23352869714018,28703237474266,144785865481702,

%T 161394923966449,168975708209638,174748809066898,207552241231357,

%U 278215179205531,312303328909720,592248982143877,812939886634531,939100782752014,983930290209021,1111161494544274

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

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

%H Brian Kehrig, <a href="/A361723/b361723.txt">Table of n, a(n) for n = 1..39</a> (terms up to 10^16)

%H Note (Apr 24 2024): An older version of the b-file missed a(33) and a(38). The present b-file is correct.

%e 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).

%o (PARI) isok(k) = sum(i=0, 99, isprime(100*k + i)) == 18; \\ _Michel Marcus_, Mar 23 2023

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

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

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

%K nonn

%O 1,1

%A _Brian Kehrig_, Mar 21 2023