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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 00:04 EST 2021. Contains 349590 sequences. (Running on oeis4.)