OFFSET
1,2
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
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 23 2011
STATUS
approved