A084066 Least integer coefficients of A(x), where 1<=a(n)<=11, such that A(x)^(1/11) consists entirely of integer coefficients.

1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 11, 11, 11, 11, 11

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.

Formula

a(k)=0 (mod 11) when k not= 0 (mod 11); a(0)=1, a(11)=1, a(22)=7, a(33)=4, a(44)=9, a(55)=5, a(66)=5, ...

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)^(1/11), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 71}] (* Robert G. Wilson v *)

Crossrefs

Cf. A083952, A083953, A083954, A083955, A083956, A083947, A083948, A083949, A083950, A084067.

Sequence in context: A171902 A337241 A045538 * A231472 A319150 A112122

Adjacent sequences: A084063 A084064 A084065 * A084067 A084068 A084069

Keyword

nonn

Author

Paul D. Hanna, May 10 2003

Extensions

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

Status

approved