

A083947


Integer coefficients of A(x), where 1<=a(n)<=7, such that A(x)^(1/7) consists entirely of integer coefficients.


12



1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7
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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)^(1/7), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)


CROSSREFS

Cf. A083952, A083953, A083954, A083955, A083956, A083948, A083949, A083950.
Sequence in context: A103983 A232127 A195413 * A269349 A112114 A031182
Adjacent sequences: A083944 A083945 A083946 * A083948 A083949 A083950


KEYWORD

nonn


AUTHOR

Paul D. Hanna, May 09 2003


EXTENSIONS

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


STATUS

approved



