cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A134779 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.

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%I A134779 #6 Mar 30 2012 18:37:07
%S A134779 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 A134779 66,68,71,74,76,78,80,82,85,88,90,92,95,98,101,104,106,108,111,114,
%U A134779 117,120,122,124,126,128,131,134,137,140,143,146,148,150,153,156,159,162,164
%N A134779 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 A134779 If the condition for a(n) is simply to be greater than a(n-1) then the sequence is A000027: the natural numbers.
%C A134779 a(n)~5/2*n.
%H A134779 Robert G. Wilson v, <a href="/A134779/b134779.txt">Table of n, a(n) for n = 0..7012</a>.
%t A134779 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 A134779 Cf. A083952, A134780.
%K A134779 nonn
%O A134779 0,2
%A A134779 _Paul D. Hanna_ & _Robert G. Wilson v_, Nov 04 2007; definition corrected Sep 19 2008