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A256472 Primes p for which there are exactly as many primes in the range [p^2, p*nextprime(p)] as there are in the range [p*nextprime(p), nextprime(p)^2], where nextprime(p) gives the next prime after prime p.

%I A256472 #15 Mar 31 2015 00:28:12
%S A256472 2,29,43,59,71,463,601,881,1049,1103,1171,1451,2311,2591,2689,2693,
%T A256472 2777,3083,3089,3917,8543,12889,13007,13799,13873,13877,15497,18457,
%U A256472 19477,20369,23017,25073,26641,29179,32801,33757,35327,41647,43987,46279,47041,49211,51577,63113
%N A256472 Primes p for which there are exactly as many primes in the range [p^2, p*nextprime(p)] as there are in the range [p*nextprime(p), nextprime(p)^2], where nextprime(p) gives the next prime after prime p.
%F A256472 a(n) = A000040(A256471(n)).
%e A256472 For p=2, 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 2 is included in the sequence.
%t A256472 Select[Prime@ Range@ 500, Count[Range[#^2, # NextPrime[#]], _?PrimeQ] == Count[Range[# NextPrime[#], NextPrime[#]^2], _?PrimeQ] &] (* _Michael De Vlieger_, Mar 30 2015 *)
%o A256472 (Scheme) (define (A256472 n) (A000040 (A256471 n)))
%Y A256472 Subsequence of A256484.
%Y A256472 Cf. A000040, A256471, A256473.
%K A256472 nonn
%O A256472 1,1
%A A256472 _Antti Karttunen_, Mar 30 2015