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

2, 6, 7, 9, 12, 15, 18, 20, 29, 34, 37, 38, 39, 43, 47, 57, 61, 62, 63, 66, 67, 77, 80, 81, 84, 86, 88, 91, 94, 103, 106, 107, 111, 113, 115, 116, 129, 133, 134, 135, 140, 145, 146, 147, 150, 151, 154, 156, 166, 173, 177, 178, 186, 188, 193, 194, 197, 201, 204, 205, 208

Offset

1,1

Links

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

Example

See A184774.

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 *)

Prog

(Python)
from math import isqrt
from itertools import count, islice
from sympy import isprime, primepi
def A184779_gen(): # generator of terms
    return map(primepi, filter(isprime, ((k<<1)+isqrt(k**2<<1) for k in count(1))))
A184779_list = list(islice(A184779_gen(), 25)) # Chai Wah Wu, Jul 28 2022

Crossrefs

Cf. A184774, A184776.

Sequence in context: A190247 A020897 A020898 * A200926 A047277 A308198

Adjacent sequences: A184776 A184777 A184778 * A184780 A184781 A184782

Keyword

nonn

Author

Clark Kimberling, Jan 21 2011

Status

approved