A186398 - OEIS

%I #32 Mar 22 2024 03:46:45

%S 186,234,319,332,340,380,384,443,444,450,469,489,542,548,554,574,611,

%T 632,645,681,683,696,716,725,731,746,749,754,805,814,829,859,873,897,

%U 907,956,963,966,977,1000,1008,1027,1044,1050

%N Numbers k such that there are 6 primes between 100*k and 100*k + 99.

%C There are 830270 possible prime patterns for centuries having 6 primes. - _Tim Johannes Ohrtmann_, Aug 27 2015

%H T. D. Noe, <a href="/A186398/b186398.txt">Table of n, a(n) for n = 1..1000</a>

%e 186 is in this sequence because there are 6 primes between 18600 and 18699 (18617, 18637, 18661, 18671, 18679 and 18691).

%t Select[Range[1100],PrimePi[100#+99]-PrimePi[100#]==6&] (* _Harvey P. Dale_, Jun 24 2018 *)

%o (PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==6, print1(n", "))); \\ _Charles R Greathouse IV_, Feb 21 2011

%o (PARI) N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==6, 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