A062409 -id:A062409 - cp's OEIS frontend

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

2, 5, 13, 19, 29, 43, 59, 67, 73, 89, 97, 103, 127, 149, 157, 163, 173, 179, 233, 239, 241, 263, 269, 271, 277, 293, 307, 331, 337, 347, 353, 383, 421, 443, 467, 521, 557, 587, 617, 619, 641, 701, 709, 733, 739, 761, 769, 823, 829, 839, 853, 883, 907, 929, 937

Offset: 1

Amarnath Murthy, Nov 09 2002

Primes not in A077545 are in A184856, since {floor(k*e)} and {floor(j*e/(e-1))} are complementary Beatty sequences (A022843 and A054385).

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

r=E; s=r/(r-1);
a[n_]:=Floor[n*r];
b[n_]:=Floor[n*s];
Table[a[n], {n, 1, 120}]  (* A022843 *)
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
(* List t1 matches A077545; list t2 matches A062409;
lists t3-t6 match A184855-A184858. *)

More terms from Sascha Kurz, Jan 12 2003

Mathematica code and crossreferences by Clark Kimberling, Jan 24 2011

A184855 Numbers m such that prime(m) is of the form (k*e); complement of A184858.

Original entry on oeis.org

1, 3, 6, 8, 10, 14, 17, 19, 21, 24, 25, 27, 31, 35, 37, 38, 40, 41, 51, 52, 53, 56, 57, 58, 59, 62, 63, 67, 68, 69, 71, 76, 82, 86, 91, 98, 102, 107, 113, 114, 116, 126, 127, 130, 131, 135, 136, 143, 145, 146, 147, 153, 155, 158, 159, 163, 168, 170, 171, 176, 177, 181, 185, 186, 187, 192, 193, 195, 196, 197, 199, 200, 202, 206, 208, 210, 214, 216, 218, 219, 222, 225, 226, 230, 232, 234, 237, 240, 243, 244, 248, 249, 252, 254

Offset: 1

Clark Kimberling, Jan 23 2011

nonn

			See A077545.

Cf. A077545, A184858.

r=E; s=r/(r-1);
a[n_]:=Floor [n*r];
b[n_]:=Floor [n*s];
Table[a[n], {n, 1, 120}]  (* A022843 *)
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
(* List t1 matches A077545; list t2 matches A062409;
lists t3-t6 match A184855-A184858. *)

cp's OEIS Frontend

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

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