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%I #31 Mar 22 2024 03:47:01
%S 21,24,31,52,53,57,66,71,77,78,79,81,102,104,108,109,110,112,113,127,
%T 133,140,146,159,175,177,180,185,197,198,205,214,232,244,254,257,263,
%U 264,266,269,270,272,274,287,292,295,298
%N Numbers k such that there are 10 primes between 100*k and 100*k + 99.
%C There are 18634704 possible prime patterns for centuries having 10 primes. - _Tim Johannes Ohrtmann_, Aug 27 2015
%H T. D. Noe, <a href="/A186402/b186402.txt">Table of n, a(n) for n = 1..1000</a>
%e 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).
%t Select[Range[300], PrimePi[100 # + 99] - PrimePi[100 #]==10 &] (* _Vincenzo Librandi_, Feb 13 2015 *)
%o (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
%o (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
%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
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