A072817 Accumulative sum of the greatest digit of n minus the least digit of n (A037904) <= 10^n.

1, 286, 4621, 56980, 640663, 6904678, 72722233, 755339992, 7774461355, 79520082490, 809705785165, 8217213032524, 83178920046367, 840306174900622, 8475694265094817, 85380606857454976, 859192675118710099, 8638686211723117474, 86794540082486097589, 871513270875022245748

Offset: 1

Author

Benoit Cloitre and Robert G. Wilson v, Aug 09 2002

Keywords

• nonn
• base

Comments

Let b(n) = sum( A037904(k),{k=1..n}), then the lim b(n)/n -> 9. Reason, as the number of digits increases, then the likelihood of the maximum digit -> 9 and the minimum digits -> 0 becomes one.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A037904.

Programs

Mathematica

f[n_] := Block[{d = IntegerDigits[n]}, Max[d] - Min[d]]; s = 0; k = 0; Do[ While[k != 10^n, k++; s = s + f[k]]; Print[s], {n, 1, 8}]

PARI

a(n)={1 + sum(w=1, n, sum(k=1, 9, (10-k)*k*((k+1)^w - 2*k^w + (k-1)^w) - k*((k+1)^(w-1) - k^(w-1))))} \\ Andrew Howroyd, Jan 28 2020

Formula

a(n) = 1 + Sum_{w=1..n} Sum_{k=1..9} (10-k)*k*((k+1)^w - 2*k^w + (k-1)^w) - k*((k+1)^(w-1) - k^(w-1)). - Andrew Howroyd, Jan 28 2020

Extensions

a(9)-a(12) from Donovan Johnson, Apr 09 2010

Terms a(13) and beyond from Andrew Howroyd, Jan 28 2020