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Search: id:A083954
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| A083954 |
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Least integer coefficients of A(x), where 1<=a(n)<=4, such that A(x)^(1/4) consists entirely of integer coefficients. |
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+0
19
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| 1, 4, 2, 4, 3, 4, 4, 4, 1, 4, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 2, 4, 2, 4, 4, 4, 4, 4, 3, 4, 2, 4, 2, 4, 2, 4, 3, 4, 2, 4, 3, 4, 2, 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 4, 2, 4, 2, 4, 1, 4, 4, 4, 1, 4, 2, 4, 4, 4, 4, 4, 1, 4, 2, 4, 3, 4, 4, 4, 4, 4, 4, 4, 3, 4, 4, 4, 2, 4, 2, 4, 2, 4, 2, 4, 1, 4, 4, 4, 1, 4, 2, 4, 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, "least 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. Is this sequence periodic?
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n = 0..5000.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
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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)^(1/4), {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, A083945, A083946.
Sequence in context: A114424 A056158 A010316 this_sequence A038702 A085062 A053051
Adjacent sequences: A083951 A083952 A083953 this_sequence A083955 A083956 A083957
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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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