A184816 Numbers m such that prime(m) is of the form k+floor(kr/s)+floor(kt/s), where r=sqrt(2), s=sqrt(3), t=sqrt(5).

1, 3, 7, 14, 18, 19, 21, 23, 24, 26, 34, 37, 39, 40, 41, 50, 53, 54, 55, 56, 65, 68, 69, 72, 78, 80, 81, 83, 86, 93, 95, 96, 98, 105, 106, 109, 113, 117, 124, 126, 129, 131, 133, 135, 137, 139, 143, 145, 148, 152, 157, 158, 159, 160, 161, 162, 168, 169, 172, 173, 174, 176, 183, 187, 190, 197, 200, 207, 208, 212, 214, 219, 229, 232, 234, 238, 242, 243, 245, 246, 257, 258, 259, 266, 267, 268, 270, 275, 276, 278, 279, 280, 281, 284

Offset

1,2

Comments

See A184812 and A184815.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Mathematica

r=2^(1/2); s=3^(1/2); t=5^(1/2);
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}]  (* A184812 *)
Table[b[n], {n, 1, 120}]  (* A184813 *)
Table[c[n], {n, 1, 120}]  (* A184814 *)
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 A184815, A184816, A184817. *)
PrimePi/@Select[Table[k+Floor[(k Sqrt[2])/Sqrt[3]]+Floor[(k Sqrt[5])/Sqrt[3]], {k, 600}], PrimeQ] (* Harvey P. Dale, Apr 25 2023 *)

Crossrefs

Cf. A184812, A184815, A184817.

Sequence in context: A342732 A218877 A179982 * A310267 A310268 A190700

Adjacent sequences: A184813 A184814 A184815 * A184817 A184818 A184819

Keyword

nonn

Author

Clark Kimberling, Jan 23 2011

Status

approved