|
| |
|
|
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
(list; graph; refs; listen; history; 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..3000.
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)^(1/6), {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: A068924 A106224 A129203 * A153607 A010494 A078333
Adjacent sequences: A083943 A083944 A083945 * A083947 A083948 A083949
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 09 2003
|
|
|
EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 26 2005
|
| |
|
|
