A360567 - OEIS

%I #28 Mar 29 2023 15:38:44

%S 3,5,7,11,23,29,43,47,53,113,127,131,157,163,167,173,179,181,277,281,

%T 283,293,347,349,353,359,367,373,379,509,521,523,541,547,821,823,827,

%U 829,839,853,857,859,863,937,941,947,953,967,971,977,983,991,1361

%N Primes p such that the nearest integer to sqrt(p) is also prime.

%H Robert Israel, <a href="/A360567/b360567.txt">Table of n, a(n) for n = 1..10000</a>

%e sqrt(11) = 3.3166247..., which when rounded is 3, and both 3 and 11 are prime, so 11 is in the sequence.

%p R:= NULL: count:= 0:

%p q:=1:

%p while count < 100 do

%p   q:= nextprime(q);

%p   p:= floor((q-1/2)^2);

%p   u:= (q+1/2)^2;

%p   while count < 100 do

%p     p:= nextprime(p);

%p     if p > u then break fi;

%p     R:= R,p; count:= count+1;

%p   od

%p od:

%p R; # _Robert Israel_, Mar 29 2023

%t Select[Prime[Range[500]],PrimeQ[Round[Sqrt[#]]] &]

%o (Python)

%o from itertools import islice

%o from math import isqrt

%o from sympy import isprime, nextprime

%o def A360567_gen(): # generator of terms

%o     p = 1

%o     while p:=nextprime(p):

%o         if isprime((m:=isqrt(p))+int(p-m*(m+1)>=1)):

%o             yield p

%o A360567_list = list(islice(A360567_gen(),20)) # _Chai Wah Wu_, Feb 27 2023

%Y Cf. A000194, A248170.

%K nonn

%O 1,1

%A _Rhys Feltman_, Feb 11 2023