A205684 Numbers k for which 5 divides prime(k)-prime(j) for some j<k; each k occurs once for each such j.

4, 6, 7, 7, 9, 9, 10, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27

Offset

1,1

Comments

For a guide to related sequences, see A205558.

Links

Table of n, a(n) for n=1..68.

Example

The first six terms match these differences:
p(4)-p(1)=7-2=5=5*1
p(6)-p(2)=13-3=10=5*2
p(7)-p(1)=17-2=15=5*3
p(7)-p(4)=17-7=10=5*2
p(9)-p(2)=23-3=20=5*4
p(9)-p(6)=23-13=10=5*2

Mathematica

s[n_] := s[n] = Prime[n]; z1 = 400; 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 = 5; t = d[c]                (* A205683 *)
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}]        (* A205684 *)
Table[j[n], {n, 1, z2}]        (* A205685 *)
Table[s[k[n]], {n, 1, z2}]     (* A205686 *)
Table[s[j[n]], {n, 1, z2}]     (* A205687 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A205688 *)
Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}] (* A205689 *)

Crossrefs

Cf. A205558, A204892, A204890, A205685, A205689.

Sequence in context: A000703 A266148 A011275 * A006185 A169788 A369802

Adjacent sequences: A205681 A205682 A205683 * A205685 A205686 A205687

Keyword

nonn

Author

Clark Kimberling, Jan 30 2012

Status

approved