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%I #6 Mar 30 2012 18:37:07
%S 1,4,6,8,11,14,16,18,21,24,27,30,33,36,38,40,43,46,49,52,55,58,61,64,
%T 66,68,71,74,76,78,80,82,85,88,90,92,95,98,101,104,106,108,111,114,
%U 117,120,122,124,126,128,131,134,137,140,143,146,148,150,153,156,159,162,164
%N Integer coefficients of A(x), where a(n) is the least integer greater than a(n-1)+2 such that A(x)^(1/2) has integer coefficients.
%C If the condition for a(n) is simply to be greater than a(n-1) then the sequence is A000027: the natural numbers.
%C a(n)~5/2*n.
%H Robert G. Wilson v, <a href="/A134779/b134779.txt">Table of n, a(n) for n = 0..7012</a>.
%t a[n_] := a[n] = Block[{k = a[n - 1] + 2, s = Sum[ a[i]*x^i, {i, 0, n - 1}]}, While[ !IntegerQ@ Last@ CoefficientList[ Series[ Sqrt[s + k*x^n], {x, 0, n}], x], k++ ]; k]; a[0] = 1; Table[ a[n], {n, 0, 63}]
%Y Cf. A083952, A134780.
%K nonn
%O 0,2
%A _Paul D. Hanna_ & _Robert G. Wilson v_, Nov 04 2007; definition corrected Sep 19 2008
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