A360567 Primes p such that the nearest integer to sqrt(p) is also prime.

3, 5, 7, 11, 23, 29, 43, 47, 53, 113, 127, 131, 157, 163, 167, 173, 179, 181, 277, 281, 283, 293, 347, 349, 353, 359, 367, 373, 379, 509, 521, 523, 541, 547, 821, 823, 827, 829, 839, 853, 857, 859, 863, 937, 941, 947, 953, 967, 971, 977, 983, 991, 1361

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

R:= NULL: count:= 0:
q:=1:
while count < 100 do
  q:= nextprime(q);
  p:= floor((q-1/2)^2);
  u:= (q+1/2)^2;
  while count < 100 do
    p:= nextprime(p);
    if p > u then break fi;
    R:= R, p; count:= count+1;
  od
od:
R; # Robert Israel, Mar 29 2023

Mathematica

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

Prog

(Python)
from itertools import islice
from math import isqrt
from sympy import isprime, nextprime
def A360567_gen(): # generator of terms
    p = 1
    while p:=nextprime(p):
        if isprime((m:=isqrt(p))+int(p-m*(m+1)>=1)):
            yield p
A360567_list = list(islice(A360567_gen(), 20)) # Chai Wah Wu, Feb 27 2023

Crossrefs

Cf. A000194, A248170.

Sequence in context: A325155 A038890 A227240 * A226017 A303705 A309520

Adjacent sequences: A360564 A360565 A360566 * A360568 A360569 A360570

Keyword

nonn

Author

Rhys Feltman, Feb 11 2023

Status

approved