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

1,1

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Complement among primes: A256484.

Cf. A000040, A256475.

Sequence in context: A044560 A039469 A124247 * A260556 A142658 A228573

Adjacent sequences: A256482 A256483 A256484 * A256486 A256487 A256488

Keyword

nonn

Author

Antti Karttunen, Mar 30 2015

Status

approved