This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109453 #13 Dec 13 2017 04:18:38 %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, %U A109453 129,133,137,141,145,150,155,160,165,170,175,180,185,190,195,201,207,213 %N A109453 Cumulative sum of initial digits of n. %H A109453 A. Cobham, <a href="https://doi.org/10.1007/BF01706087">Uniform Tag Sequences</a>, 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}] (* _Robert G. Wilson v_, Aug 30 2005 *) %t A109453 Accumulate[First/@(IntegerDigits/@Range[70])] (* _Harvey P. Dale_, Jan 11 2016 *) %o A109453 (PARI) a(n) = sum(k=1, n, digits(k)[1]); \\ _Michel Marcus_, Dec 13 2017 %Y A109453 Partial sums of A000030. %K A109453 base,easy,nonn %O A109453 1,2 %A A109453 _Jonathan Vos Post_, Aug 27 2005 %E A109453 Corrected by _Robert G. Wilson v_, Aug 30 2005