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%I #12 Oct 31 2013 12:17:23
%S 1,6,3,2,3,6,6,6,3,4,6,6,6,6,3,4,6,6,3,6,6,2,3,6,6,6,3,4,6,6,2,6,6,6,
%T 6,6,6,6,3,4,6,6,4,6,6,2,6,6,4,6,3,2,3,6,6,6,3,4,3,6,3,6,3,4,6,6,2,6,
%U 3,6,3,6,1,6,6,4,6,6,2,6,6,2,6,6,3,6,3,4,6,6,1,6,6,6,6,6,6,6,3,2,6,6,6,6,3
%N Least integer coefficients of A(x), where 1<=a(n)<=6, such that A(x)^(1/6) consists entirely of integer coefficients.
%C 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?
%H Robert G. Wilson v, <a href="/A083946/b083946.txt">Table of n, a(n) for n = 0..3000</a>.
%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
%t 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)^(1/6), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* _Robert G. Wilson v_ *)
%Y Cf. A083952, A083953, A083954, A083945.
%K nonn
%O 0,2
%A _Paul D. Hanna_, May 09 2003
%E More terms from _Robert G. Wilson v_, Jul 26 2005
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