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A072817
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Accumulative sum of the greatest digit of n minus the least digit of n (A037904) <= 10^n.
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1
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1, 286, 4621, 56980, 640663, 6904678, 72722233, 755339992, 7774461355, 79520082490, 809705785165, 8217213032524, 83178920046367, 840306174900622, 8475694265094817, 85380606857454976, 859192675118710099, 8638686211723117474, 86794540082486097589, 871513270875022245748
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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