A217971 a(n) = 2^(2*n+1) * (2*n+1)*n^(2*n).

24, 2560, 653184, 301989888, 220000000000, 231818611654656, 333360204766740480, 627189298506124754944, 1495163506861268427866112, 4404019200000000000000000000, 15705682358754099640245749284864, 66686788842514206222454073642188800, 332430457331186494783020411573611003904

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Oct 16 2012

Keywords

• nonn

Comments

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).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100
• Vladimir Shevelev and Peter J. C. Moses, A family of digit functions with large periods, arXiv:1209.5705 [math.NT], 2012.

Crossrefs

Cf. A214458, A218085.

Programs

Mathematica

Table[2^(2*n + 1)*(2*n + 1)*n^(2*n), {n, 15}] (* Wesley Ivan Hurt, Apr 28 2020 *)

Maxima

A217971(n):=2^(2*n+1)*(2*n+1)*n^(2*n)$ makelist(A217971(n),n,1,10); /* Martin Ettl, Nov 15 2012 */

PARI

a(n) = {2^(2*n+1) * (2*n+1)*n^(2*n)} \\ Andrew Howroyd, Apr 28 2020

Extensions

Terms a(11) and beyond from Andrew Howroyd, Apr 28 2020