Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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