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Search: id:A109453
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| A109453 |
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Cumulative sum of initial digits of n. |
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+0
6
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| 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
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.
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FORMULA
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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).
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MATHEMATICA
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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}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Aug 30 2005)
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CROSSREFS
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Partial sums of A000030.
Sequence in context: A130488 A061076 A054632 this_sequence A037123 A062918 A113168
Adjacent sequences: A109450 A109451 A109452 this_sequence A109454 A109455 A109456
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KEYWORD
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base,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 27 2005
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EXTENSIONS
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Corrected by Robert G. Wilson v (rgwv(at)rgwv.com), Aug 30 2005
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