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A083947
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Integer coefficients of A(x), where 1<=a(n)<=7, such that A(x)^(1/7) consists entirely of integer coefficients.
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12
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1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| Robert G. Wilson v, Table of n, a(n) for n = 0..3000.
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MATHEMATICA
| 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)^(1/7), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A083952, A083953, A083954, A083955, A083956, A083948, A083949, A083950.
Sequence in context: A019799 A103983 A195413 * A112114 A031182 A106705
Adjacent sequences: A083944 A083945 A083946 * A083948 A083949 A083950
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 09 2003
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 26 2005
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