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A154280
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List of pairs: {a(n),b(n)}: f(n)=A004001(n); a(n)=f(n)+a(n-1); b(n)=f(n)*b(n-1);
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0
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0, 1, 1, 1, 2, 1, 4, 2, 6, 4, 9, 12, 13, 48, 17, 192, 21, 768, 26, 3840, 32, 23040, 39, 161280, 46, 1128960, 54, 9031680, 62, 72253440, 70, 578027520, 78, 4624220160, 87, 41617981440, 97, 416179814400, 108, 4577977958400, 120, 54935735500800, 132
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| There are primes associated with the product sequence:
Flatten[Table[If[PrimeQ[b[n] - 1], b[n] - 1, If[PrimeQ[b[n] + 1], b[ n] + 1, {}]], {n, 0, 30}]].
{2, 2, 2, 3, 3, 11, 47, 191, 769, 23039, 161281, 9031681, 41617981439,
8569974738124801, 119979646333747199}
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FORMULA
| f(n)=A004001(n);
a(n)=f(n)+a(n-1);
b(n)=f(n)*b(n-1);
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MATHEMATICA
| Clear[a, b, f, n];
(*A004001*) f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[f[n - 1]] + f[n - f[n - 1]];
a[0] = 0; a[n_] := a[n] = f[n] + a[n - 1];
b[0] = 1; b[1] = 1; b[n_] := b[n] = (f[n])*b[n - 1];
Flatten[Table[{a[n], b[n]}, {n, 0, 30}]]
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CROSSREFS
| A004001
Sequence in context: A194747 A065423 A008733 * A004795 A161268 A176837
Adjacent sequences: A154277 A154278 A154279 * A154281 A154282 A154283
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KEYWORD
| nonn,uned,tabf
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 06 2009
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