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.

2, 29, 43, 59, 71, 463, 601, 881, 1049, 1103, 1171, 1451, 2311, 2591, 2689, 2693, 2777, 3083, 3089, 3917, 8543, 12889, 13007, 13799, 13873, 13877, 15497, 18457, 19477, 20369, 23017, 25073, 26641, 29179, 32801, 33757, 35327, 41647, 43987, 46279, 47041, 49211, 51577, 63113

Offset

1,1

Links

Table of n, a(n) for n=1..44.

Formula

a(n) = A000040(A256471(n)).

Example

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.

Mathematica

Select[Prime@ Range@ 500, Count[Range[#^2, # NextPrime[#]], _?PrimeQ] == Count[Range[# NextPrime[#], NextPrime[#]^2], _?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

Prog

(Scheme) (define (A256472 n) (A000040 (A256471 n)))

Crossrefs

Subsequence of A256484.

Cf. A000040, A256471, A256473.

Sequence in context: A078329 A340633 A252892 * A330895 A105893 A366692

Adjacent sequences: A256469 A256470 A256471 * A256473 A256474 A256475

Keyword

nonn

Author

Antti Karttunen, Mar 30 2015

Status

approved