A184815 - OEIS

A184815

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

2, 4, 10, 12, 13, 16, 22, 29, 30, 36, 42, 44, 45, 49, 52, 57, 59, 60, 64, 70, 71, 76, 82, 84, 90, 91, 92, 97, 101, 103, 108, 111, 114, 115, 119, 123, 125, 138, 140, 142, 149, 150, 165, 171, 178, 180, 182, 185, 189, 191, 192, 193, 195, 198, 205, 211, 215, 217, 220, 222, 224, 233, 235, 236, 247, 248, 249, 252, 254, 255, 264, 265, 269, 273, 286, 295, 301, 302, 306, 307, 309, 316, 318, 325, 326, 327, 328, 329, 332, 336

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OFFSET

1,1

COMMENTS

A184815, A184816, and A184817 partition the primes:

A184815: 3,7,29,37,... of the form n+[ns/r]+[nt/r].

A184816: 2,5,17,... of the form n+[nr/s]+[nt/s].

A184817: 11,13,19,23,31,... of the form n+[nr/t]+[ns/t].

The Mathematica code can be easily modified to print primes in the three classes.

LINKS

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

EXAMPLE

See A184812.

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. *)

CROSSREFS

Cf. A184812, A184816, A184817.

Sequence in context: A101519 A227204 A249446 * A290473 A356664 A138940

Adjacent sequences: A184812 A184813 A184814 * A184816 A184817 A184818

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 23 2011

STATUS

approved