A256484 Primes p for which there are at least as many primes in the range [p*nextprime(p), nextprime(p)^2] as in the range [p^2, p*nextprime(p)], where nextprime(p) gives the next prime after prime p.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 173, 199, 211, 233, 239, 241, 251, 263, 269, 281, 293, 311, 317, 331, 337, 349, 353, 359, 379, 383, 397, 401, 409, 421, 431, 433, 439, 449, 461, 463, 467, 487, 491, 499, 509

Offset: 1

Author

Antti Karttunen, Mar 30 2015

Keywords

• nonn

Examples

			For p=3, we have in the range [3*3, 3*5] two primes, {11, 13}, and in the latter range [3*5, 5*5] we have three primes {17, 19, 23}, thus 3 is included in the sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3457

Crossrefs

Complement among primes: A256485.

Cf. A256472 (a subsequence).

Cf. A000040, A256474.

Programs

Mathematica

Select[Prime@ Range@ 100, Count[Range[# NextPrime[#], NextPrime[#]^2], ?PrimeQ] >= Count[Range[#^2, # NextPrime[#]], ?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

Scheme

(define (A256484 n) (A000040 (A256474 n)))

Formula

a(n) = A000040(A256474(n)).