OFFSET
0,2
COMMENTS
More generally, the sequence: "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. Are these sequences ever periodic?
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 0..3000.
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)^(1/12), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 81}] (* Robert G. Wilson v *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 10 2003
EXTENSIONS
More terms from Robert G. Wilson v, Jul 26 2005
STATUS
approved