cp's OEIS Frontend

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

%I A184776 #19 Jul 29 2022 09:56:20
%S A184776 1,3,4,5,8,10,11,13,14,16,17,19,21,22,23,24,25,26,27,28,30,31,32,33,
%T A184776 35,36,40,41,42,44,45,46,48,49,50,51,52,53,54,55,56,58,59,60,64,65,68,
%U A184776 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
%N A184776 Numbers m such that prime(m) is of the form floor(k*sqrt(2)); complement of A184779.
%H A184776 G. C. Greubel, <a href="/A184776/b184776.txt">Table of n, a(n) for n = 1..10000</a>
%e A184776 See A184774.
%t A184776 r=2^(1/2); s=r/(r-1);
%t A184776 a[n_]:=Floor [n*r];  (* A001951 *)
%t A184776 b[n_]:=Floor [n*s];  (* A001952 *)
%t A184776 Table[a[n],{n,1,120}]
%t A184776 t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1,a[n]]], {n,1,600}]; t1
%t A184776 t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2,n]], {n,1,600}]; t2
%t A184776 t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3,n]],{n,1,300}]; t3
%t A184776 t4={}; Do[If[PrimeQ[b[n]], AppendTo[t4,b[n]]],{n,1,600}]; t4
%t A184776 t5={}; Do[If[PrimeQ[b[n]], AppendTo[t5,n]],{n,1,600}]; t5
%t A184776 t6={}; Do[If[MemberQ[t4, Prime[n]], AppendTo[t6,n]],{n,1,300}]; t6
%t A184776 (* the lists t1,t2,t3,t4,t5,t6 match the sequences
%t A184776 A184774, A184775, A184776 ,A184777, A184778, A184779 *)
%o A184776 (Python)
%o A184776 from itertools import count, islice
%o A184776 from math import isqrt
%o A184776 from sympy import primepi, isprime
%o A184776 def A184776_gen(): # generator of terms
%o A184776     return map(primepi,filter(isprime,(isqrt(k**2<<1) for k in count(1))))
%o A184776 A184776_list = list(islice(A184776_gen(),25)) # _Chai Wah Wu_, Jul 28 2022
%Y A184776 Cf. A184774, A184775, A184779.
%K A184776 nonn
%O A184776 1,2
%A A184776 _Clark Kimberling_, Jan 21 2011