A135932 Primes whose integer square root remainder is also prime.

3, 7, 11, 19, 23, 41, 43, 47, 67, 71, 83, 103, 107, 113, 149, 151, 157, 163, 167, 199, 227, 263, 269, 331, 337, 347, 353, 419, 431, 443, 487, 491, 503, 521, 587, 593, 599, 607, 613, 617, 619, 683, 719, 787, 797, 821, 827, 907, 911, 919, 929, 937, 941, 947

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

Table of n, a(n) for n=1..54.

Wikipedia, Integer square root

Mathematica

f[n_]:=n-(Floor[Sqrt[n]])^2; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]], AppendTo[lst, p]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)

Prog

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

Crossrefs

Sequence in context: A018805 A191037 A292083 * A231847 A105876 A354801

Adjacent sequences: A135929 A135930 A135931 * A135933 A135934 A135935

Keyword

nonn

Author

Harry J. Smith, Dec 07 2007

Status

approved