login
A186402
Numbers k such that there are 10 primes between 100*k and 100*k + 99.
1
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved