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Search: id:A084066
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| A084066 |
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Least integer coefficients of A(x), where 1<=a(n)<=11, such that A(x)^(1/11) consists entirely of integer coefficients. |
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+0
8
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| 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 11, 11, 11, 11, 11
(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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FORMULA
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a(k)=0 (mod 11) when k not= 0 (mod 11); a(0)=1, a(11)=1, a(22)=7, a(33)=4, a(44)=9, a(55)=5, a(66)=5, ...
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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)^(1/11), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 71}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A083952, A083953, A083954, A083955, A083956, A083947, A083948, A083949, A083950, A084067.
Sequence in context: A087994 A100755 A045538 this_sequence A112122 A010850 A113587
Adjacent sequences: A084063 A084064 A084065 this_sequence A084067 A084068 A084069
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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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