A256473 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.

3, 31, 47, 61, 73, 467, 607, 883, 1051, 1109, 1181, 1453, 2333, 2593, 2693, 2699, 2789, 3089, 3109, 3919, 8563, 12893, 13009, 13807, 13877, 13879, 15511, 18461, 19483, 20389, 23021, 25087, 26647, 29191, 32803, 33767, 35339, 41651, 43991, 46301, 47051, 49223, 51581, 63127

Offset: 1

Author

Antti Karttunen, Mar 30 2015

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000040, A065091, A256471, A256472.

Programs

Mathematica

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 *)

Scheme

(define (A256473 n) (A000040 (+ 1 (A256471 n))))

Formula

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