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A205705 Numbers k for which 8 divides prime(k)-prime(j) for some j<k; each k occurs once for each such j. 8
5, 6, 8, 8, 9, 10, 10, 11, 11, 12, 12, 12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26 (list; graph; refs; listen; history; text; internal format)
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(5)-p(2)=11-3=8=8*1

p(6)-p(3)=13-5=8=8*1

p(8)-p(2)=19-3=16=8*2

p(8)-p(5)=19-11=8=8*1

p(9)-p(4)=23-7=16=8*2

p(10)-p(3)=29-5=24=8*3

MATHEMATICA

s[n_] := s[n] = Prime[n]; z1 = 900; z2 = 70;

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 = 8; t = d[c]             (* A205704 *)

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}]         (* A205705 *)

Table[j[n], {n, 1, z2}]         (* A205706 *)

Table[s[k[n]], {n, 1, z2}]      (* A205707 *)

Table[s[j[n]], {n, 1, z2}]      (* A205708 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]      (* A205709 *)

Table[(s[k[n]] - s[j[n]])/c, {n, 1, z2}]  (* A205710 *)

CROSSREFS

Cf. A205558, A204892, A204890, A205706, A205710.

Sequence in context: A099149 A197480 A180443 * A270653 A299538 A201512

Adjacent sequences:  A205702 A205703 A205704 * A205706 A205707 A205708

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 31 2012

STATUS

approved

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Last modified August 21 06:01 EDT 2019. Contains 326162 sequences. (Running on oeis4.)