login
Primes of the form p - floor(sqrt(p)), p prime.
1

%I #11 Jul 07 2022 02:11:52

%S 2,3,5,13,19,31,37,41,59,71,97,103,137,139,151,197,241,313,331,389,

%T 401,419,487,499,563,569,577,593,683,701,769,811,877,881,907,911,1019,

%U 1031,1129,1153,1283,1291,1409,1433,1451,1567,1579,1597,1627,1741,1747,1759

%N Primes of the form p - floor(sqrt(p)), p prime.

%C Primes k such that k + floor(sqrt(k + floor(sqrt(k)))) is prime (see A000037). - _Ivan N. Ianakiev_, Jun 23 2022

%H Charles R Greathouse IV, <a href="/A173830/b173830.txt">Table of n, a(n) for n = 1..10000</a>

%t f[n_]:=n-Floor[Sqrt[n]];lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,f[p]]],{n,7!}];lst

%o (PARI) forprime(p=2,1e4,if(isprime(t=p-sqrtint(p)),print1(t", "))) \\ _Charles R Greathouse IV_, Apr 15 2012

%Y Cf. A086086, A000037.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 25 2010