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A204900 Least k such that n divides s(k)-s(j) for some j in [1,k), where s(k) is the k-th odd prime. 23
2, 2, 4, 3, 5, 4, 6, 4, 8, 5, 9, 6, 9, 6, 11, 7, 11, 8, 12, 8, 14, 9, 15, 9, 15, 9, 16, 10, 17, 11, 18, 11, 19, 11, 20, 12, 21, 12, 22, 13, 23, 14, 23, 14, 24, 15, 24, 15, 25, 15, 27, 16, 28, 16, 29, 16, 30, 17, 31, 18, 30, 18, 31, 18, 32, 19, 32, 19, 34, 20, 34, 21, 34 (list; graph; refs; listen; history; text; internal format)
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]; z1 = 400; z2 = 50;

Table[s[n], {n, 1, 30}]      (* A065091 *)

u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]

Table[u[m], {m, 1, z1}]      (* A204898 *)

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}]      (* A204899 *)

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}]      (* A204900 *)

Table[j[n], {n, 1, z2}]      (* A204901 *)

Table[s[k[n]], {n, 1, z2}]   (* A204902 *)

Table[s[j[n]], {n, 1, z2}]   (* A204903 *)

Table[s[k[n]] - s[j[n]], {n, 1, z2}]     (* A204904 *)

Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A000034 conjectured *)

CROSSREFS

Cf. A000040, A065091, A204892.

Sequence in context: A215675 A132802 A268353 * A070803 A071693 A225381

Adjacent sequences:  A204897 A204898 A204899 * A204901 A204902 A204903

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 20 2012

STATUS

approved

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Last modified July 26 10:24 EDT 2017. Contains 289835 sequences.