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%I #13 Dec 13 2017 04:18:38
%S 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 67,69,71,73,75,78,81,84,87,90,93,96,99,102,105,109,113,117,121,125,
%U 129,133,137,141,145,150,155,160,165,170,175,180,185,190,195,201,207,213
%N Cumulative sum of initial digits of n.
%H A. Cobham, <a href="https://doi.org/10.1007/BF01706087">Uniform Tag Sequences</a>, Mathematical Systems Theory, 6 (1972), 164-192.
%F 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 f[n_] := Sum[ Floor[i / 10^Floor[Log[10, i]]], {i, n}]; Table[ f[n], {n, 62}] (* or *)
%t a[0] = 0; a[n_] := a[n] = (a[n - 1] + First[ IntegerDigits[ n]]); Table[ a[n], {n, 62}] (* _Robert G. Wilson v_, Aug 30 2005 *)
%t Accumulate[First/@(IntegerDigits/@Range[70])] (* _Harvey P. Dale_, Jan 11 2016 *)
%o (PARI) a(n) = sum(k=1, n, digits(k)[1]); \\ _Michel Marcus_, Dec 13 2017
%Y Partial sums of A000030.
%K base,easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Aug 27 2005
%E Corrected by _Robert G. Wilson v_, Aug 30 2005
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