A083948 Integer coefficients of A(x), where 1<=a(n)<=8, such that A(x)^(1/8) consists entirely of integer coefficients.

1, 8, 4, 8, 2, 8, 4, 8, 7, 8, 8, 8, 4, 8, 8, 8, 3, 8, 8, 8, 2, 8, 8, 8, 1, 8, 8, 8, 8, 8, 8, 8, 6, 8, 4, 8, 6, 8, 4, 8, 6, 8, 8, 8, 4, 8, 8, 8, 4, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 8, 8, 8, 6, 8, 8, 8, 8, 8, 4, 8, 6, 8, 4, 8, 8, 8, 8, 8, 6, 8, 8, 8, 7, 8, 4, 8, 8, 8, 4, 8, 3, 8, 4, 8, 4, 8, 4, 8, 3

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. Are these sequences 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)^(1/8), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)

Crossrefs

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

Sequence in context: A199266 A347145 A205383 * A021848 A021545 A141614

Adjacent sequences: A083945 A083946 A083947 * A083949 A083950 A083951

Keyword

nonn

Author

Paul D. Hanna, May 09 2003

Extensions

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

Status

approved