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 A083953 Least integer coefficients of A(x), where 1<=a(n)<=3, such that A(x)^(1/3) consists entirely of integer coefficients. 23
 1, 3, 3, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 3, 3, 2, 3, 3, 2, 3, 3, 1, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 3, 3, 1, 3, 3, 2, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3, 2, 3, 3, 1, 3, 3, 3, 3, 3, 1, 3, 3 (list; graph; refs; listen; history; text; internal format)
 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. Is this sequence periodic? LINKS 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. FORMULA a(k)=1 at k=0, 3, 12, 21, 51, 57, 60, 63, 66, ...; a(k)=2 at k=15, 18, 24, 30, 39, 42, 48, 54, ... 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)^(1/3), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v, Jul 25 2005 *) CROSSREFS Cf. A083952, A083954, A083945, A083946. Sequence in context: A278265 A171369 A111629 * A066400 A125562 A092040 Adjacent sequences:  A083950 A083951 A083952 * A083954 A083955 A083956 KEYWORD nonn AUTHOR Paul D. Hanna, May 09 2003 EXTENSIONS More terms from Robert G. Wilson v, Jul 25 2005 STATUS approved

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Last modified May 19 13:39 EDT 2019. Contains 323393 sequences. (Running on oeis4.)