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.

A083951 Least increasing integer coefficients such that A(x)^(1/3) has only integer coefficients.

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%I A083951 #11 Jul 19 2015 01:39:09
%S A083951 1,3,6,7,9,12,13,15,18,21,24,27,28,30,33,34,36,39,41,42,45,47,48,51,
%T A083951 52,54,57,60,63,66,69,72,75,77,78,81,83,84,87,88,90,93,94,96,99,100,
%U A083951 102,105,108,111,114,116,117,120,121,123,126,127,129,132,133,135,138,139
%N A083951 Least increasing integer coefficients such that A(x)^(1/3) has only integer coefficients.
%C A083951 a(k) == 1 (mod 3) at k=0,3,6,12,15,24,39,42,45,54,57,60,63,66,... a(k) == 2 (mod 3) at k=18,21,33,36,51,...
%H A083951 Robert G. Wilson v, <a href="/A083951/b083951.txt">Table of n, a(n) for n = 0..5000</a>.
%t A083951 a[0] = 1; a[n_] := a[n] = Block[{k = a[n - 1] + 1, s = Sum[ a[i]*x^i, {i, 0, n - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^n)^(1/3), {x, 0, n}], x]]] != True, k++ ]; k]; Array[ a, 70] (* _Robert G. Wilson v_, Sep 19 2008 *)
%Y A083951 Cf. A083349, A083953.
%K A083951 nonn
%O A083951 0,2
%A A083951 _Paul D. Hanna_, May 09 2003
%E A083951 Three non-ascending values in the range 77 to 84 replaced with those from the b-file. - _R. J. Mathar_, Jan 14 2009