A184776 Numbers m such that prime(m) is of the form floor(k*sqrt(2)); complement of A184779.

1, 3, 4, 5, 8, 10, 11, 13, 14, 16, 17, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 64, 65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 82, 83, 85, 87, 89, 90, 92, 93, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 108, 109, 110, 112, 114, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 130, 131, 132, 136, 137, 138, 139, 141, 142, 143, 144

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, A184775, 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 *)

Python

from itertools import count, islice
from math import isqrt
from sympy import primepi, isprime
def A184776_gen(): # generator of terms
    return map(primepi,filter(isprime,(isqrt(k**2<<1) for k in count(1))))
A184776_list = list(islice(A184776_gen(),25)) # Chai Wah Wu, Jul 28 2022