A186408 Numbers k such that there are 16 primes between 100*k and 100*k + 99.

2, 3, 6, 10, 42, 58, 194, 230, 12463, 8392963, 24662691, 37400476, 163061323, 205481131, 278399797, 313114319, 481863166, 494959102, 656914015, 776749247, 960655996, 980373049, 1097546872, 1156724143, 2013136112, 2245034146, 3416649829, 3606810631, 4141180699, 5928231877, 6569717174, 6594050440, 7240502155, 7492029097, 8995086259

Offset: 1

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

• nonn

Comments

There are 6699888 possible prime patterns for centuries having 16 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			2 is in this sequence because there are 16 primes between 200 and 299 (211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283 and 293).
		

Links

• Brian Kehrig, Table of n, a(n) for n = 1..1000

Crossrefs

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

Cf. A181098 (no primes), A186393-A186407 (1 to 15 primes), A186509 (17 primes), A361723 (18 primes).

Programs

PARI

for(n=1, 1e6, if(sum(k=100*n,100*(n+1), ispseudoprime(k))==16, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011

PARI

N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==16, print1((N\100)-1,", ")); s=1; N=100*(p\100+1),s++)) \\ Charles R Greathouse IV, Feb 21 2011

Extensions

a(9)-a(12) from Charles R Greathouse IV, Feb 21 2011

a(13)-a(35) from T. D. Noe, Feb 23 2011