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A083948 Integer coefficients of A(x), where 1<=a(n)<=8, such that A(x)^(1/8) consists entirely of integer coefficients. 15

%I

%S 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,

%T 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,

%U 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

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

%C 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?

%H Robert G. Wilson v, <a href="/A083948/b083948.txt">Table of n, a(n) for n = 0..3000</a>.

%t 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_ *)

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, May 09 2003

%E More terms from _Robert G. Wilson v_, Jul 26 2005

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Last modified November 14 01:24 EST 2019. Contains 329108 sequences. (Running on oeis4.)