A205153 Least k such that n divides s(k)-s(j) for some j<k, where s(j)=(prime(j+1) + prime(j+2))/2.

2, 2, 3, 4, 3, 4, 6, 4, 5, 8, 5, 6, 9, 6, 7, 10, 7, 9, 10, 8, 9, 8, 14, 9, 10, 9, 11, 10, 14, 10, 20, 14, 11, 16, 11, 12, 20, 12, 13, 22, 13, 16, 17, 14, 16, 14, 15, 16, 17, 15, 16, 15, 30, 16, 17, 16, 18, 17, 23, 17, 20, 31, 18, 20, 18, 19, 20, 19, 21, 20, 22, 20, 24

Offset

1,1

Comments

See A204892 for a discussion and guide to related sequences.

Links

Table of n, a(n) for n=1..73.

Mathematica

s[n_] := s[n] = (Prime[n + 1] + Prime[n + 2])/2; z1 = 1100; z2 = 80;
Table[s[n], {n, 1, 30}]     (* A024675 *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}]     (* A204980 *)
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] = First[Delete[w[n], Position[w[n], 0]]]
Table[d[n], {n, 1, z2}]     (* A205152 *)
k[n_] := k[n] = Floor[(3 + Sqrt[8 d[n] - 1])/2]
m[n_] := m[n] = Floor[(-1 + Sqrt[8 n - 7])/2]
j[n_] := j[n] = d[n] - m[d[n]] (m[d[n]] + 1)/2
Table[k[n], {n, 1, z2}]       (* A205153 *)
Table[j[n], {n, 1, z2}]       (* A205154 *)
Table[s[k[n]], {n, 1, z2}]    (* A205372 *)
Table[s[j[n]], {n, 1, z2}]    (* A205373 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205374 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}]  (* A205375 *)

Crossrefs

Cf. A024675, A204892, A205375.

Sequence in context: A336200 A032355 A308597 * A300302 A091257 A216622

Adjacent sequences: A205150 A205151 A205152 * A205154 A205155 A205156

Keyword

nonn

Author

Clark Kimberling, Jan 26 2012

Status

approved