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Search: id:A084067
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| A084067 |
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Integer coefficients of A(x), where 1<=a(n)<=12, such that A(x)^(1/12) consists entirely of integer coefficients. |
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12
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| 1, 12, 6, 4, 9, 12, 4, 12, 12, 8, 6, 12, 6, 12, 12, 12, 12, 12, 8, 12, 9, 12, 12, 12, 12, 12, 6, 12, 6, 12, 10, 12, 6, 12, 12, 12, 2, 12, 6, 8, 6, 12, 12, 12, 12, 4, 12, 12, 8, 12, 12, 8, 3, 12, 4, 12, 12, 4, 12, 12, 9, 12, 6, 4, 6, 12, 4, 12, 12, 12, 12, 12, 2, 12, 6, 12, 3, 12, 6, 12, 3, 8
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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More generally, the sequence: "integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m>0. Are these sequences ever periodic?
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MATHEMATICA
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a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/12), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 81}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A083952, A083953, A083954, A083955, A083956, A083947 A083948, A083949, A083950, A084066.
Sequence in context: A033332 A051725 A070292 this_sequence A075247 A040135 A004015
Adjacent sequences: A084064 A084065 A084066 this_sequence A084068 A084069 A084070
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 10 2003
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 26 2005
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