

A135930


Primes whose integer square root is also prime.


1



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
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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)^21]), [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



