A192361 Primes p such that number of primes in the range (p-sqrt(p), p] is equal to number of primes in the range (p, p+sqrt(p)].

2, 11, 29, 37, 41, 71, 97, 103, 131, 191, 229, 257, 263, 311, 331, 347, 373, 379, 443, 491, 541, 593, 643, 727, 733, 739, 797, 821, 929, 967, 991, 1013, 1019, 1097, 1163, 1171, 1201, 1213, 1217, 1259, 1291, 1297, 1373, 1451, 1481, 1531, 1553, 1571, 1583, 1657, 1709, 1777, 1831, 1873, 1949, 1999, 2053

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 28 2011

Keywords

• nonn

Examples

			a(1)=2 because 2 in range (2-sqrt(2), 2] and 3 in range (2, 2+sqrt(2)],
a(2)=11 because 7 in range (11-sqrt(11), 11] and 13 in range (11, 11+sqrt(11)].
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A058188.

Programs

Mathematica

npeQ[p_]:=Module[{p1=PrimePi[p],p2=PrimePi[p-Sqrt[p]],p3=PrimePi[p+Sqrt[p]]},p3-p1 == p1-p2]; Select[Prime[Range[400]],npeQ] (* Harvey P. Dale, Jan 31 2024 *)

PARI

is(p)=2*primepi(p)==primepi(p+sqrt(p))+primepi(p-sqrt(p))
select(isA192361,primes(1000)) \\ Charles R Greathouse IV, Jun 29 2011

Extensions

Missing terms a(3) and a(7) inserted, a(19)-a(57) added by Charles R Greathouse IV, Jun 29 2011