%I #9 Mar 30 2015 21:43:00

%S 41,97,101,163,167,179,181,191,193,197,223,227,229,257,271,277,283,

%T 307,313,347,367,373,389,419,443,457,479,503,521,547,563,577,587,593,

%U 599,641,643,659,661,673,683,691,719,811,821,823,829,839,857,859,877,907,929,937,983,1009,1021,1031,1051,1063,1087,1091,1093,1151,1153

%N Primes p for which there are more primes in range [p^2, p*nextprime(p)] than in range [p*nextprime(p), nextprime(p)^2], where nextprime(p) gives the next prime after prime p.

%H Antti Karttunen, <a href="/A256485/b256485.txt">Table of n, a(n) for n = 1..3084</a>

%F a(n) = A000040(A256475(n)).

%e For p=41, we have in range [41*41, 41*43] (1681 .. 1763) 11 primes: {1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759}, while in the latter range [41*43, 43*43] (1763 .. 1849) we have 9 primes: {1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847}, thus 41 is included in the sequence.

%t Select[Prime@ Range@ 200, Count[Range[#^2, # NextPrime[#]], _?PrimeQ] > Count[Range[# NextPrime[#], NextPrime[#]^2], _?PrimeQ] &] (* _Michael De Vlieger_, Mar 30 2015 *)

%o (Scheme) (define (A256485 n) (A000040 (A256475 n)))

%Y Complement among primes: A256484.

%Y Cf. A000040, A256475.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 30 2015