A186399 Numbers k such that there are 7 primes between 100*k and 100*k + 99.

59, 95, 142, 165, 167, 191, 196, 206, 212, 242, 252, 281, 283, 297, 299, 318, 349, 357, 372, 385, 394, 406, 407, 414, 417, 425, 431, 433, 452, 457, 459, 462, 470, 480, 482, 504, 510, 533, 551, 555, 563, 585, 595, 599, 604

Offset

1,1

Comments

There are 2459376 possible prime patterns for centuries having 7 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Links

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

Example

59 is in this sequence because there are 7 primes between 5900 and 5999 (5903, 5923, 5927, 5939, 5953, 5981 and 5987).

Mathematica

Select[Range[610], PrimePi[100#+99]-PrimePi[100#]==7&] (* Harvey P. Dale, Nov 05 2011 *)

Prog

(PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==7, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
(PARI) N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==7, 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: A097459 A145291 A136076 * A039431 A043254 A044034

Adjacent sequences: A186396 A186397 A186398 * A186400 A186401 A186402

Keyword

nonn

Author

Tim Johannes Ohrtmann, Feb 20 2011

Status

approved