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

1,1

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Complement among primes: A256485.

Cf. A256472 (a subsequence).

Cf. A000040, A256474.

Sequence in context: A078133 A341661 A268513 * A238242 A197298 A211654

Adjacent sequences: A256481 A256482 A256483 * A256485 A256486 A256487

Keyword

nonn

Author

Antti Karttunen, Mar 30 2015

Status

approved