%I #11 Mar 31 2015 00:28:22

%S 3,31,47,61,73,467,607,883,1051,1109,1181,1453,2333,2593,2693,2699,

%T 2789,3089,3109,3919,8563,12893,13009,13807,13877,13879,15511,18461,

%U 19483,20389,23021,25087,26647,29191,32803,33767,35339,41651,43991,46301,47051,49223,51581,63127

%N Odd primes p for which there are exactly as many primes in the range [prevprime(p)^2, prevprime(p)*p] as there are in the range [prevprime(p)*p, p^2], where prevprime(p) gives the previous prime before prime p.

%F a(n) = A065091(A256471(n)) = A000040(1+A256471(n)).

%e For p=3, we have in the range [2*2, 2*3] just one prime {5}, and also in the latter range [2*3, 3*3] just one prime {7}, thus 3 is included in the sequence.

%t Select[Prime@ Range[2, 500], Count[Range[NextPrime[#, -1]^2, # NextPrime[#, -1]], _?PrimeQ] == Count[Range[# NextPrime[#, -1], #^2], _?PrimeQ] &] (* _Michael De Vlieger_, Mar 30 2015 *)

%o (Scheme) (define (A256473 n) (A000040 (+ 1 (A256471 n))))

%Y Cf. A000040, A065091, A256471, A256472.

%K nonn

%O 1,1

%A _Antti Karttunen_, Mar 30 2015