A186402 Numbers k such that there are 10 primes between 100*k and 100*k + 99.

21, 24, 31, 52, 53, 57, 66, 71, 77, 78, 79, 81, 102, 104, 108, 109, 110, 112, 113, 127, 133, 140, 146, 159, 175, 177, 180, 185, 197, 198, 205, 214, 232, 244, 254, 257, 263, 264, 266, 269, 270, 272, 274, 287, 292, 295, 298

Offset

1,1

Comments

There are 18634704 possible prime patterns for centuries having 10 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

21 is in this sequence because there are 10 primes between 2100 and 2199 (2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161 and 2179).

Mathematica

Select[Range[300], PrimePi[100 # + 99] - PrimePi[100 #]==10 &] (* Vincenzo Librandi, Feb 13 2015 *)

Prog

(PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==10, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
(PARI) N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==10, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

Crossrefs

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

Cf. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Sequence in context: A344806 A295692 A033267 * A346294 A330736 A303814

Adjacent sequences: A186399 A186400 A186401 * A186403 A186404 A186405

Keyword

nonn

Author

Tim Johannes Ohrtmann, Feb 20 2011

Status

approved