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Search: id:A083948
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| A083948 |
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Integer coefficients of A(x), where 1<=a(n)<=8, such that A(x)^(1/8) consists entirely of integer coefficients. |
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+0
15
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| 1, 8, 4, 8, 2, 8, 4, 8, 7, 8, 8, 8, 4, 8, 8, 8, 3, 8, 8, 8, 2, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 6, 8, 4, 8, 6, 8, 4, 8, 6, 8, 8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 6, 8, 8, 8, 8, 8, 4, 8, 6, 8, 4, 8, 8, 8, 8, 8, 6, 8, 8, 8, 7, 8, 4, 8, 8, 8, 4, 8, 3, 8, 4, 8, 4, 8, 4, 8, 3
(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. Are these sequences periodic?
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 0..3000.
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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)^(1/8), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A083952, A083953, A083954, A083955, A083956, A083947, A083949, A083950.
Adjacent sequences: A083945 A083946 A083947 this_sequence A083949 A083950 A083951
Sequence in context: A110233 A019684 A019867 this_sequence A021848 A021545 A141614
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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 09 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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