

A083949


Integer coefficients of A(x), where 1<=a(n)<=9, such that A(x)^(1/9) consists entirely of integer coefficients.


13



1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 9, 9, 6, 9, 9, 6, 9, 9, 9, 9, 9, 6, 9, 9, 6, 9, 9, 9, 9, 9, 3, 9, 9, 3, 9, 9, 2, 9, 9, 6, 9, 9, 6, 9, 9, 7, 9, 9, 9, 9, 9, 9, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 6, 9, 9, 6, 9, 9, 5, 9, 9, 9, 9, 9, 9, 9, 9, 3, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 6, 9, 9, 6, 9, 9, 7, 9, 9, 6, 9, 9
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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)^(1/9), {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, A083948, A083950.
Sequence in context: A179102 A153505 A088398 * A007471 A180012 A172504
Adjacent sequences: A083946 A083947 A083948 * A083950 A083951 A083952


KEYWORD

nonn


AUTHOR

Paul D. Hanna, May 09 2003


EXTENSIONS

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


STATUS

approved



