

A083946


Least integer coefficients of A(x), where 1<=a(n)<=6, such that A(x)^(1/6) consists entirely of integer coefficients.


12



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, 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, 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
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OFFSET

0,2


COMMENTS

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?


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..3000.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of nth Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 17321745.


MATHEMATICA

a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n1}]}, 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 *)


CROSSREFS

Cf. A083952, A083953, A083954, A083945.
Sequence in context: A244815 A226579 A129203 * A254593 A153607 A010494
Adjacent sequences: A083943 A083944 A083945 * A083947 A083948 A083949


KEYWORD

nonn


AUTHOR

Paul D. Hanna, May 09 2003


EXTENSIONS

More terms from Robert G. Wilson v, Jul 26 2005


STATUS

approved



