A135930 Primes whose integer square root is also prime.

5, 7, 11, 13, 29, 31, 53, 59, 61, 127, 131, 137, 139, 173, 179, 181, 191, 193, 293, 307, 311, 313, 317, 367, 373, 379, 383, 389, 397, 541, 547, 557, 563, 569, 571, 853, 857, 859, 863, 877, 881, 883, 887, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021

Offset

1,1

Comments

The integer square root of an integer x >= 0 can be defined as floor(sqrt(x)) and the remainder of this as x - (floor(sqrt(x)))^2.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Wikipedia, Integer square root

Maple

map(p -> select(isprime, [$p^2+1..(p+1)^2-1]), [seq(ithprime(i), i=1..10)]); # Robert Israel, Jun 08 2018

Mathematica

f[n_]:=PrimeQ[IntegerPart[Sqrt[n]]]; lst={}; Do[p=Prime[n]; If[f[p], AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 12 2009 *)
Select[Prime[Range[200]], PrimeQ[IntegerPart[Sqrt[#]]]&] (* Harvey P. Dale, Jun 23 2016 *)

Prog

(PARI) { forprime(p=2, 2000, isr = sqrtint(p); if (isprime(isr), print1(p, ", ") ) ) }

Crossrefs

Cf. A000196 (integer square root).

Sequence in context: A135774 A180946 A265006 * A163429 A339953 A220951

Adjacent sequences: A135927 A135928 A135929 * A135931 A135932 A135933

Keyword

nonn

Author

Harry J. Smith, Dec 07 2007

Status

approved