A184777 Primes of the form 2k + floor(k*sqrt(2)).

3, 13, 17, 23, 37, 47, 61, 71, 109, 139, 157, 163, 167, 191, 211, 269, 283, 293, 307, 317, 331, 389, 409, 419, 433, 443, 457, 467, 491, 563, 577, 587, 607, 617, 631, 641, 727, 751, 757, 761, 809, 829, 839, 853, 863, 877, 887, 911, 983, 1031, 1051, 1061, 1109, 1123, 1171, 1181, 1201, 1229, 1249, 1259, 1283, 1297, 1307, 1321, 1399, 1423, 1427, 1433, 1447, 1451, 1471, 1481, 1543, 1553, 1567, 1597, 1601, 1621, 1669, 1693, 1741, 1789, 1823, 1847, 1867, 1877, 1901

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
def A184777_gen(): # generator of terms
    return filter(isprime, ((k<<1)+isqrt(k**2<<1) for k in count(1)))
A184777_list = list(islice(A184777_gen(), 25)) # Chai Wah Wu, Jul 28 2022

Crossrefs

Cf. A184774, A184778, A184779.

Sequence in context: A038883 A141188 A019347 * A339329 A045433 A216535

Adjacent sequences: A184774 A184775 A184776 * A184778 A184779 A184780

Keyword

nonn

Author

Clark Kimberling, Jan 21 2011

Status

approved