A077545 - OEIS

%I #13 Aug 22 2024 04:49:58

%S 2,5,13,19,29,43,59,67,73,89,97,103,127,149,157,163,173,179,233,239,

%T 241,263,269,271,277,293,307,331,337,347,353,383,421,443,467,521,557,

%U 587,617,619,641,701,709,733,739,761,769,823,829,839,853,883,907,929,937

%N Primes of the form floor(k*e).

%C 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 r=E; s=r/(r-1);

%t a[n_]:=Floor[n*r];

%t b[n_]:=Floor[n*s];

%t Table[a[n], {n, 1, 120}]  (* A022843 *)

%t t1={}; Do[If[PrimeQ[a[n]], AppendTo[t1, a[n]]], {n, 1, 600}]; t1

%t t2={}; Do[If[PrimeQ[a[n]], AppendTo[t2, n]], {n, 1, 600}]; t2

%t t3={}; Do[If[MemberQ[t1, Prime[n]], AppendTo[t3, n]], {n, 1, 300}]; t3

%t t4={}; Do[If[PrimeQ[b[n]], AppendTo[t4, b[n]]], {n, 1, 600}]; t4

%t t5={}; Do[If[PrimeQ[b[n]], AppendTo[t5, n]], {n, 1, 600}]; t5

%t t6={}; Do[If[MemberQ[t4, Prime[n]], AppendTo[t6, n]], {n, 1, 300}]; t6

%t (* List t1 matches A077545; list t2 matches A062409;

%t lists t3-t6 match A184855-A184858. *)

%Y Cf. A062409, A184855, A184856, A184587, A184858.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 09 2002

%E More terms from _Sascha Kurz_, Jan 12 2003

%E Mathematica code and crossreferences by _Clark Kimberling_, Jan 24 2011