A109453 Cumulative sum of initial digits of n.

1, 3, 6, 10, 15, 21, 28, 36, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 109, 113, 117, 121, 125, 129, 133, 137, 141, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 201, 207, 213

Offset

1,2

Links

Table of n, a(n) for n=1..62.

A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.

Formula

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).

Mathematica

f[n_] := Sum[ Floor[i / 10^Floor[Log[10, i]]], {i, n}]; Table[ f[n], {n, 62}] (* or *)
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 *)
Accumulate[First/@(IntegerDigits/@Range[70])] (* Harvey P. Dale, Jan 11 2016 *)

Prog

(PARI) a(n) = sum(k=1, n, digits(k)[1]); \\ Michel Marcus, Dec 13 2017

Crossrefs

Partial sums of A000030.

Sequence in context: A130488 A061076 A054632 * A217627 A037123 A062918

Adjacent sequences: A109450 A109451 A109452 * A109454 A109455 A109456

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Aug 27 2005

Extensions

Corrected by Robert G. Wilson v, Aug 30 2005

Status

approved