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 A102685 Partial sums of A055640. 30
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The total number of nonzero digits occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012 LINKS Hieronymus Fischer, Table of n, a(n) for n = 0..10000 FORMULA From Hieronymus Fischer, Jun 06 2012 (Start): a(n) = (1/2)*sum_{j=1..m+1} (floor((n/10^j)+0.9)*(2n + 2 + (0.8 - floor((n/10^j)+0.9))*10^j) - floor(n/10^j)*(2n + 2 - (floor(n/10^j)+1) * 10^j)), where m = floor(log_10(n)). a(n) = (n+1)*A055640(n) + (1/2)*sum_{j=1..m+1} ((8*floor((n/10^j)+0.9)/10 + floor(n/10^j))*10^j - (floor((n/10^j)+0.9)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)). a(10^m-1) = 9*m*10^(m-1). (This is the total number of nonzero digits occurring in all the numbers with <= m digits.) G.f.: g(x) = (1/(1-x)^2) * sum_{j>=0} (x^10^j - x^(10*10^j))/(1-x^10^(j+1)). (End) CROSSREFS Cf. A027868, A054899, A055640, A055641, A102669-A102684, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Cf. A000120, A000788, A023416, A059015 (for base 2). Sequence in context: A317622 A331400 A067082 * A032960 A117804 A088235 Adjacent sequences:  A102682 A102683 A102684 * A102686 A102687 A102688 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 03 2005 STATUS approved

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Last modified August 4 10:01 EDT 2021. Contains 346446 sequences. (Running on oeis4.)