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| NAME
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allocatedLeast k such that n divides s(k)-s(j) for some j satisfying 1<=j<k, where s(j)=2*j^2-j, the jth Clarkhexagonal Kimberlingnumber.
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| DATA
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2, 3, 3, 5, 2, 5, 3, 9, 3, 5, 4, 6, 4, 3, 5, 17, 5, 7, 6, 6, 6, 4, 7, 11, 7, 11, 4, 11, 8, 5, 9, 33, 9, 14, 8, 9, 10, 6, 5, 13, 11, 12, 12, 5, 7, 7, 13, 18, 9, 14, 6, 12, 14, 8, 11, 13, 8, 23, 16, 6
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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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| MATHEMATICA
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s[n_] := s[n] = 2 n^2 - n; z1 = 500; z2 = 60;
Table[s[n], {n, 1, 30}] (* A000384, hexagonal numbers *)
u[m_] := u[m] = Flatten[Table[s[k] - s[j], {k, 2, z1}, {j, 1, k - 1}]][[m]]
Table[u[m], {m, 1, z1}] (* A205128 *)
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}] (* A205129 *)
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}] (* A205130 *)
Table[j[n], {n, 1, z2}] (* A205131 *)
Table[s[k[n]], {n, 1, z2}] (* A205132 *)
Table[s[j[n]], {n, 1, z2}] (* A205133 *)
Table[s[k[n]] - s[j[n]], {n, 1, z2}] (* A205134 *)
Table[(s[k[n]] - s[j[n]])/n, {n, 1, z2}] (* A205135 *)
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| CROSSREFS
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Cf. A000384, A204892, A205135.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jan 25 2012
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| STATUS
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approved
editing
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