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%I #30 Mar 22 2024 03:44:07
%S 41,43,70,73,83,89,99,115,117,120,123,128,132,138,143,150,158,161,163,
%T 168,171,172,193,200,202,208,209,216,222,223,225,229,233,237,239,246,
%U 276,278,282,288,290,294,300,302,303,304
%N Numbers k such that there are 9 primes between 100*k and 100*k + 99.
%C There are 11555200 possible prime patterns for centuries having 9 primes. - _Tim Johannes Ohrtmann_, Aug 27 2015
%H T. D. Noe, <a href="/A186401/b186401.txt">Table of n, a(n) for n = 1..1000</a>
%e 41 is in this sequence because there are 9 primes between 4100 and 4199 (4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159 and 4177).
%t Select[Range[350],PrimePi[100#+99]-PrimePi[100#]==9&] (* _Harvey P. Dale_, Sep 05 2023 *)
%o (PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==9, print1(n", "))); \\ _Charles R Greathouse IV_, Feb 21 2011
%o (PARI) N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==9, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ _Charles R Greathouse IV_, Feb 21 2011
%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), A361723 (18 primes).
%K nonn
%O 1,1
%A _Tim Johannes Ohrtmann_, Feb 20 2011
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