A186403 - OEIS

%I #32 Mar 22 2024 03:47:25

%S 13,25,29,32,34,38,39,44,51,61,65,72,74,80,87,90,92,93,97,100,107,111,

%T 114,121,130,134,139,154,170,181,182,183,184,187,190,192,195,210,213,

%U 217,218,227,249,251,261,262,267,279,280

%N Numbers k such that there are 11 primes between 100*k and 100*k + 99.

%C There are 24942742 possible prime patterns for centuries having 11 primes. - _Tim Johannes Ohrtmann_, Aug 27 2015

%H T. D. Noe, <a href="/A186403/b186403.txt">Table of n, a(n) for n = 1..1000</a>

%e 13 is in this sequence because there are 11 primes between 1300 and 1399 (1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381 and 1399).

%t Select[Range[300],PrimePi[100#+99]-PrimePi[100#]==11&] (* _Harvey P. Dale_, Jul 26 2011 *)

%o (PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==11, print1(n", "))); \\ _Charles R Greathouse IV_, Feb 21 2011

%o (PARI) N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==11, 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