A083950 Integer coefficients of A(x), where 1<=a(n)<=10, such that A(x)^(1/10) consists entirely of integer coefficients.

1, 10, 5, 10, 10, 2, 5, 10, 10, 10, 3, 10, 5, 10, 10, 2, 10, 10, 10, 10, 5, 10, 5, 10, 5, 8, 5, 10, 5, 10, 8, 10, 10, 10, 10, 4, 5, 10, 10, 10, 7, 10, 10, 10, 5, 2, 10, 10, 5, 10, 7, 10, 5, 10, 5, 4, 10, 10, 10, 10, 7, 10, 10, 10, 10, 2, 5, 10, 5, 10, 9, 10, 5, 10, 5, 6, 5, 10, 10, 10, 8

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)^(1/10), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 80}] (* Robert G. Wilson v *)

Crossrefs

Cf. A083952, A083953, A083954, A083952, A083956, A083947, A083948, A083949.

Sequence in context: A241146 A296420 A078267 * A045617 A158486 A280154

Adjacent sequences: A083947 A083948 A083949 * A083951 A083952 A083953

Keyword

nonn

Author

Paul D. Hanna, May 09 2003

Extensions

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

Status

approved