_Clark Kimberling (ck6(AT)evansville.edu), _, Jan 23 2011

proposed

approved

allocated for Clark KimberlingNumbers m such that prime(m) is of the form k+floor(ks/r)+floor(kt/r), where r=log(2), s=log(3), t=log(5).

6, 8, 9, 14, 16, 25, 28, 31, 32, 33, 36, 52, 57, 61, 65, 69, 71, 73, 78, 79, 82, 83, 95, 97, 111, 112, 113, 118, 121, 125, 126, 136, 140, 146, 147, 151, 154, 155, 156, 160, 167, 171, 176, 179, 180, 183, 185, 193, 194, 197, 209, 215, 220, 225, 233, 234, 240, 244, 249, 250, 255, 256, 260, 261, 262, 265, 268, 271, 287, 289, 293, 302, 312, 317, 324, 325, 329, 331, 335, 339, 357, 360, 361, 363, 365, 367, 369, 370, 374, 385, 386, 389, 392, 394, 396, 400, 404, 406, 408, 417

1,1

A184874, A184875, A184876 partition the primes.

A184874: 7,23,41,... of the form n+[ns/r]+[nt/r].

A184875: 3,11,19,31,... of the form n+[nr/s]+[nt/s].

A184876: 2,5,13,17,29,... of the form n+[nr/t]+[ns/t].

The Mathematica code can be easily modified to print

primes in the three classes.

See A184871.

r=Log[2]; s=Log[3]; t=Log[5];

a[n_]:=n+Floor [n*s/r]+Floor[n*t/r];

b[n_]:=n+Floor [n*r/s]+Floor[n*t/s];

c[n_]:=n+Floor[n*r/t]+Floor[n*s/t];

Table[a[n], {n, 1, 120}] (* A184871 *)

Table[b[n], {n, 1, 120}] (* A184872 *)

Table[c[n], {n, 1, 120}] (* A184873 *)

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, 600}]; 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, 600}]; t6

t7={}; Do[If[PrimeQ[c[n]], AppendTo[t7, c[n]]], {n, 1, 600}]; t7;

t8={}; Do[If[PrimeQ[c[n]], AppendTo[t8, n]], {n, 1, 600}]; t8;

t9={}; Do[If[MemberQ[t7, Prime[n]], AppendTo[t9, n]], {n, 1, 600}]; t9

(* Lists t3, t6, t9 match A184874, A184875, A184876. *)

Cf. A184871, A184872, A184873, A184875, A184876.

allocated

nonn

Clark Kimberling (ck6(AT)evansville.edu), Jan 23 2011

approved

proposed

allocated for Clark Kimberling

allocated

approved