A086085 Primes p such that p + floor(sqrt(p)) is prime.

2, 5, 19, 37, 41, 47, 71, 103, 151, 167, 197, 277, 331, 349, 401, 419, 487, 499, 577, 593, 607, 617, 619, 683, 701, 811, 829, 907, 911, 937, 941, 947, 953, 1031, 1061, 1451, 1493, 1511, 1627, 1657, 1669, 1789, 1831, 1847, 1949, 1973, 2161, 2309, 2333, 2341

Offset

1,1

Links

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

Example

a(3)=19 because 19 is prime and 19 + floor(sqrt(19)) = 19 + floor(4.358898944) = 19 + 4 = 23, which is prime.

Mathematica

f[n_]:=Floor[Sqrt[n]]+n; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)
Select[Prime[Range[400]], PrimeQ[#+Floor[Sqrt[#]]]&] (* Harvey P. Dale, Apr 09 2026 *)

Crossrefs

Sequence in context: A090700 A227632 A105889 * A138250 A140761 A077323

Adjacent sequences: A086082 A086083 A086084 * A086086 A086087 A086088

Keyword

nonn

Author

Chuck Seggelin, Jul 08 2003

Extensions

More terms from R. J. Mathar, Oct 31 2008

Status

approved