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A083954 Least integer coefficients of A(x), where 1<=a(n)<=4, such that A(x)^(1/4) consists entirely of integer coefficients. 19
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; 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>0. 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.

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)^(1/4), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)

CROSSREFS

Cf. A083952, A083953, A083945, A083946.

Sequence in context: A246819 A056158 A010316 * A038702 A085062 A053051

Adjacent sequences:  A083951 A083952 A083953 * A083955 A083956 A083957

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 09 2003

EXTENSIONS

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

STATUS

approved

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Last modified May 21 00:51 EDT 2019. Contains 323428 sequences. (Running on oeis4.)