%I A109453
%S A109453 1,3,6,10,15,21,28,36,45,46,47,48,49,50,51,52,53,54,55,57,59,61,63,65,
%T A109453 67,69,71,73,75,78,81,84,87,90,93,96,99,102,105,109,113,117,121,125,129,
%U A109453 133,137,141,145,150,155,160,165,170,175,180,185,190,195,201,207,213
%N A109453 Cumulative sum of initial digits of n.
%D A109453 A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 
               164-192.
%F A109453 a(n) = Sum_{i=1..n} A000030(i). a(n) = Sum_{i=1..n} [i / 10^([log_10(i)])] 
               where [] denotes floor and log_10(i) is the logarithm is base 10. 
               a(n+1) = a(n) + first-digit-of(n+1).
%t A109453 f[n_] := Sum[ Floor[i / 10^Floor[Log[10, i]]], {i, n}]; Table[ f[n], 
               {n, 62}] (* or *)
%t A109453 a[0] = 0; a[n_] := a[n] = (a[n - 1] + First[ IntegerDigits[ n]]); Table[ 
               a[n], {n, 62}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Aug 30 
               2005)
%Y A109453 Partial sums of A000030.
%Y A109453 Sequence in context: A130488 A061076 A054632 this_sequence A037123 A062918 
               A113168
%Y A109453 Adjacent sequences: A109450 A109451 A109452 this_sequence A109454 A109455 
               A109456
%K A109453 base,easy,nonn
%O A109453 1,2
%A A109453 Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 27 2005
%E A109453 Corrected by Robert G. Wilson v (rgwv(at)rgwv.com), Aug 30 2005