

A205560


Numbers k for which 3 divides prime(k)prime(j) for some j<k; each k occurs once for each such j.


8



3, 5, 5, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19
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OFFSET

1,1


COMMENTS

For a guide to related sequences, see A205558.


LINKS

Table of n, a(n) for n=1..70.


EXAMPLE

The first six terms match these differences:
p(3)p(1)=52=3=3*1
p(5)p(1)=112=9=3*3
p(5)p(3)=115=6=3*2
p(6)p(4)=137=6=3*2
p(7)p(1)=172=15=3*5
p(7)p(3)=175=12=3*4


MATHEMATICA

s[n_] := s[n] = Prime[n]; z1 = 200; z2 = 80;
f[n_] := f[n] = Floor[(1 + Sqrt[8 n  7])/2];
Table[s[n], {n, 1, 30}] (* A000040 *)
u[m_] := u[m] = Flatten[Table[s[k]  s[j], {k, 2, z1}, {j, 1, k  1}]][[m]]
Table[u[m], {m, 1, z1}] (* A204890 *)
v[n_, h_] := v[n, h] = If[IntegerQ[u[h]/n], h, 0]
w[n_] := w[n] = Table[v[n, h], {h, 1, z1}]
d[n_] := d[n] = Delete[w[n], Position[w[n], 0]]
c = 3; t = d[c] (* A205559 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 t[[n]]  1])/2]
j[n_] := j[n] = t[[n]]  f[t][[n]] (f[t[[n]]] + 1)/2
Table[k[n], {n, 1, z2}] (* A205560 *)
Table[j[n], {n, 1, z2}] (* A205547 *)
Table[s[k[n]], {n, 1, z2}] (* A205673 *)
Table[s[j[n]], {n, 1, z2}] (* A205674 *)
Table[s[k[n]]  s[j[n]], {n, 1, z2}] (* A205557 *)
Table[(s[k[n]]  s[j[n]])/c, {n, 1, z2}] (* A205675 *)


CROSSREFS

Cf. A204892, A205547, A204890, A205675.
Sequence in context: A029912 A272756 A322350 * A195939 A317587 A235647
Adjacent sequences: A205557 A205558 A205559 * A205561 A205562 A205563


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jan 30 2012


STATUS

approved



