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A077545 Primes of the form floor(k*e).

%I A077545 #13 Aug 22 2024 04:49:58
%S A077545 2,5,13,19,29,43,59,67,73,89,97,103,127,149,157,163,173,179,233,239,
%T A077545 241,263,269,271,277,293,307,331,337,347,353,383,421,443,467,521,557,
%U A077545 587,617,619,641,701,709,733,739,761,769,823,829,839,853,883,907,929,937
%N A077545 Primes of the form floor(k*e).
%C A077545 Primes not in A077545 are in A184856, since {floor(k*e)} and {floor(j*e/(e-1))} are complementary Beatty sequences (A022843 and A054385).
%t A077545 r=E; s=r/(r-1);
%t A077545 a[n_]:=Floor[n*r];
%t A077545 b[n_]:=Floor[n*s];
%t A077545 Table[a[n], {n, 1, 120}]  (* A022843 *)
%t A077545 t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1, a[n]]], {n, 1, 600}]; t1
%t A077545 t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2, n]], {n, 1, 600}]; t2
%t A077545 t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3, n]], {n, 1, 300}]; t3
%t A077545 t4={}; Do[If[PrimeQ[b[n]], AppendTo[t4, b[n]]], {n, 1, 600}]; t4
%t A077545 t5={}; Do[If[PrimeQ[b[n]], AppendTo[t5, n]], {n, 1, 600}]; t5
%t A077545 t6={}; Do[If[MemberQ[t4, Prime[n]], AppendTo[t6, n]], {n, 1, 300}]; t6
%t A077545 (* List t1 matches A077545; list t2 matches A062409;
%t A077545 lists t3-t6 match A184855-A184858. *)
%Y A077545 Cf. A062409, A184855, A184856, A184587, A184858.
%K A077545 base,nonn
%O A077545 1,1
%A A077545 _Amarnath Murthy_, Nov 09 2002
%E A077545 More terms from _Sascha Kurz_, Jan 12 2003
%E A077545 Mathematica code and crossreferences by _Clark Kimberling_, Jan 24 2011