Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Jul 19 2015 01:39:09
%S 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 52,54,57,60,63,66,69,72,75,77,78,81,83,84,87,88,90,93,94,96,99,100,
%U 102,105,108,111,114,116,117,120,121,123,126,127,129,132,133,135,138,139
%N Least increasing integer coefficients such that A(x)^(1/3) has only integer coefficients.
%C 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 Robert G. Wilson v, <a href="/A083951/b083951.txt">Table of n, a(n) for n = 0..5000</a>.
%t 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 Cf. A083349, A083953.
%K nonn
%O 0,2
%A _Paul D. Hanna_, May 09 2003
%E Three non-ascending values in the range 77 to 84 replaced with those from the b-file. - _R. J. Mathar_, Jan 14 2009