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Search: id:A073851
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| A073851 |
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Cumulative sum of initial digits of (n base 5). |
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+0
1
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| 0, 1, 3, 6, 10, 11, 12, 13, 14, 15, 17, 19, 21, 23, 25, 28, 31, 34, 37, 40, 44, 48, 52, 56, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121
(list; graph; listen)
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OFFSET
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0,3
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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[from i = 0 to n] Initial-Digit(A007091(n)). a(n) = SUM{from i = 0 to n} first-digit{(i base 4)} where (i base 5) = A007091(i); A007091(0)=0, A007091(i)=10* A007091(i/5) if i==0 (mod 5), A007091(i)= A007091(i-1)+1 otherwise. a(n) = SUM{from i = 1 to n} [n / 5^([log_5(n)])] where [ ] denotes floor and log_5(n) is the logarithm is base 5. a(n+1) = a(n) + first-digit-of((n+1) (base 5)).
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EXAMPLE
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n Base 5 Init Cum Sum
0 0 0 0
1 1 1 1
2 2 2 3
3 3 3 6
4 4 4 10
5 10 1 11
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CROSSREFS
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Cf. A007091, A109453.
Sequence in context: A130483 A115012 A135738 this_sequence A043321 A123053 A138289
Adjacent sequences: A073848 A073849 A073850 this_sequence A073852 A073853 A073854
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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 28 2005
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