A184778 Numbers k such that 2k + floor(k*sqrt(2)) is prime.

1, 4, 5, 7, 11, 14, 18, 21, 32, 41, 46, 48, 49, 56, 62, 79, 83, 86, 90, 93, 97, 114, 120, 123, 127, 130, 134, 137, 144, 165, 169, 172, 178, 181, 185, 188, 213, 220, 222, 223, 237, 243, 246, 250, 253, 257, 260, 267, 288, 302, 308, 311, 325, 329, 343, 346, 352, 360, 366, 369, 376

Offset: 1

Author

Clark Kimberling, Jan 21 2011

Keywords

• nonn

Examples

			See A184774.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A184774, A184777, A184779.

Programs

Mathematica

r=2^(1/2); s=r/(r-1);
a[n_]:=Floor [n*r];  (* A001951 *)
b[n_]:=Floor [n*s];  (* A001952 *)
Table[a[n],{n,1,120}]
t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]], {n,1,600}]; t1
t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]], {n,1,600}]; t2
t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3,n]],{n,1,300}]; t3
t4={}; Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}]; t4
t5={}; Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}]; t5
t6={}; Do[If[MemberQ[t4, Prime[n]], AppendTo[t6,n]],{n,1,300}]; t6
(* the lists t1,t2,t3,t4,t5,t6 match the sequences
A184774, A184775, A184776 ,A184777, A184778, A184779 *)

PARI

is(n)=isprime(sqrtint(2*n^2)+2*n) \\ Charles R Greathouse IV, May 22 2017

Python

from itertools import count, islice
from math import isqrt
from sympy import isprime
def A184778_gen(): # generator of terms
    return filter(lambda k:isprime((k<<1)+isqrt(k**2<<1)), count(1))
A184778_list = list(islice(A184778_gen(),25)) # Chai Wah Wu, Jul 28 2022