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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 (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..70.

EXAMPLE

The first six terms match these differences:

p(3)-p(1)=5-2=3=3*1

p(5)-p(1)=11-2=9=3*3

p(5)-p(3)=11-5=6=3*2

p(6)-p(4)=13-7=6=3*2

p(7)-p(1)=17-2=15=3*5

p(7)-p(3)=17-5=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

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Last modified December 7 20:29 EST 2019. Contains 329849 sequences. (Running on oeis4.)