A205698 Numbers k for which 7 divides prime(k)-prime(j) for some j<k; each k occurs once for each such j.

7, 8, 9, 11, 11, 12, 12, 13, 14, 15, 15, 16, 17, 17, 17, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 31, 31, 31, 31, 32, 32, 32, 32, 32

Offset

1,1

Comments

For a guide to related sequences, see A205558.

Links

Table of n, a(n) for n=1..67.

Example

The first six terms match these differences:
p(7)-p(2)=17-3=14=7*2
p(8)-p(3)=19-5=14=7*2
p(9)-p(1)=23-2=21=7*3
p(11)-p(2)=31-3=28=7*4
p(11)-p(7)=31-17=14=7*2
p(12)-p(1)=37-2=35=7*5

Mathematica

s[n_] := s[n] = Prime[n]; z1 = 1200; 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 = 7; t = d[c]                (* A205697 *)
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}]         (* A205698 *)
Table[j[n], {n, 1, z2}]         (* A205699 *)
Table[s[k[n]], {n, 1, z2}]      (* A205700 *)
Table[s[j[n]], {n, 1, z2}]      (* A205701 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205702 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205703 *)

Crossrefs

Cf. A205558, A204892, A204890, A205699, A205703.

Sequence in context: A106108 A120309 A035705 * A210147 A340741 A097338

Adjacent sequences: A205695 A205696 A205697 * A205699 A205700 A205701

Keyword

nonn

Author

Clark Kimberling, Jan 31 2012

Status

approved