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

%I A184779 #17 Jul 29 2022 09:56:35
%S A184779 2,6,7,9,12,15,18,20,29,34,37,38,39,43,47,57,61,62,63,66,67,77,80,81,
%T A184779 84,86,88,91,94,103,106,107,111,113,115,116,129,133,134,135,140,145,
%U A184779 146,147,150,151,154,156,166,173,177,178,186,188,193,194,197,201,204,205,208
%N A184779 Numbers m such that prime(m) is of the form 2k + floor(k*sqrt(2)); complement of A184776.
%H A184779 G. C. Greubel, <a href="/A184779/b184779.txt">Table of n, a(n) for n = 1..10000</a>
%e A184779 See A184774.
%t A184779 r=2^(1/2); s=r/(r-1);
%t A184779 a[n_]:=Floor [n*r];  (* A001951 *)
%t A184779 b[n_]:=Floor [n*s];  (* A001952 *)
%t A184779 Table[a[n],{n,1,120}]
%t A184779 t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]], {n,1,600}]; t1
%t A184779 t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]], {n,1,600}]; t2
%t A184779 t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3,n]],{n,1,300}]; t3
%t A184779 t4={}; Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}]; t4
%t A184779 t5={}; Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}]; t5
%t A184779 t6={}; Do[If[MemberQ[t4, Prime[n]], AppendTo[t6,n]],{n,1,300}]; t6
%t A184779 (* the lists t1,t2,t3,t4,t5,t6 match the sequences
%t A184779 A184774, A184775, A184776 ,A184777, A184778, A184779 *)
%o A184779 (Python)
%o A184779 from math import isqrt
%o A184779 from itertools import count, islice
%o A184779 from sympy import isprime, primepi
%o A184779 def A184779_gen(): # generator of terms
%o A184779     return map(primepi,filter(isprime,((k<<1)+isqrt(k**2<<1) for k in count(1))))
%o A184779 A184779_list = list(islice(A184779_gen(),25)) # _Chai Wah Wu_, Jul 28 2022
%Y A184779 Cf. A184774, A184776.
%K A184779 nonn
%O A184779 1,1
%A A184779 _Clark Kimberling_, Jan 21 2011