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A204900
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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.
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23
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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
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OFFSET
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1,1
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COMMENTS
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See A204892 for a discussion and guide to related sequences
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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