

A083950


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


13



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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, n1}]}, 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



