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%I #28 Apr 29 2020 07:37:27
%S 24,2560,653184,301989888,220000000000,231818611654656,
%T 333360204766740480,627189298506124754944,1495163506861268427866112,
%U 4404019200000000000000000000,15705682358754099640245749284864,66686788842514206222454073642188800,332430457331186494783020411573611003904
%N a(n) = 2^(2*n+1) * (2*n+1)*n^(2*n).
%C Let S_(2*n+1)(m) denote difference between multiples of 2*n+1 in interval [0,m), m>=1, with even and odd digit sums in base 2*n. As is shown in the Shevelev and Moses link, a recursion for S_(2*n+1)(m) is connected with the periodicity of a special digit function, the smallest period of which is a(n).
%H Andrew Howroyd, <a href="/A217971/b217971.txt">Table of n, a(n) for n = 1..100</a>
%H Vladimir Shevelev and Peter J. C. Moses, <a href="http://arxiv.org/abs/1209.5705">A family of digit functions with large periods</a>, arXiv:1209.5705 [math.NT], 2012.
%t Table[2^(2*n + 1)*(2*n + 1)*n^(2*n), {n, 15}] (* _Wesley Ivan Hurt_, Apr 28 2020 *)
%o (Maxima) A217971(n):=2^(2*n+1)*(2*n+1)*n^(2*n)$ makelist(A217971(n),n,1,10); /* _Martin Ettl_, Nov 15 2012 */
%o (PARI) a(n) = {2^(2*n+1) * (2*n+1)*n^(2*n)} \\ _Andrew Howroyd_, Apr 28 2020
%Y Cf. A214458, A218085.
%K nonn
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Oct 16 2012
%E Terms a(11) and beyond from _Andrew Howroyd_, Apr 28 2020
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