A256485 Primes p for which there are more primes in range [p^2, p*nextprime(p)] than in range [p*nextprime(p), nextprime(p)^2], where nextprime(p) gives the next prime after prime p.

41, 97, 101, 163, 167, 179, 181, 191, 193, 197, 223, 227, 229, 257, 271, 277, 283, 307, 313, 347, 367, 373, 389, 419, 443, 457, 479, 503, 521, 547, 563, 577, 587, 593, 599, 641, 643, 659, 661, 673, 683, 691, 719, 811, 821, 823, 829, 839, 857, 859, 877, 907, 929, 937, 983, 1009, 1021, 1031, 1051, 1063, 1087, 1091, 1093, 1151, 1153

Offset: 1

Author

Antti Karttunen, Mar 30 2015

Keywords

• nonn

Examples

			For p=41, we have in range [41*41, 41*43] (1681 .. 1763) 11 primes: {1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759}, while in the latter range [41*43, 43*43] (1763 .. 1849) we have 9 primes: {1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847}, thus 41 is included in the sequence.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3084

Crossrefs

Complement among primes: A256484.

Cf. A000040, A256475.

Programs

Mathematica

Select[Prime@ Range@ 200, Count[Range[#^2, # NextPrime[#]], ?PrimeQ] > Count[Range[# NextPrime[#], NextPrime[#]^2], ?PrimeQ] &] (* Michael De Vlieger, Mar 30 2015 *)

Scheme

(define (A256485 n) (A000040 (A256475 n)))

Formula

a(n) = A000040(A256475(n)).