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A109834
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Startorial numbers: product of initial digits of integers 1 through n.
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1
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1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 362880, 725760, 1451520, 2903040, 5806080, 11612160, 23224320, 46448640, 92897280, 185794560, 371589120, 1114767360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is a base 10 sequence; the equivalent exists for other bases. For base 1 and base 2, this gives the all-one sequence (A000012).
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REFERENCES
| A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.
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FORMULA
| a(n) = Prod{from i = 1 to n} A000030(i). a(n+1) = a(n) * InitialDigitOf(n). a(n) = Prod{from i = 1 to n} [i / 10^([log_10(i)])] where [] denotes floor and log_10(i) is the logarithm of i in base 10.
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EXAMPLE
| a(30) = 1*2*3*4*5*6*7*8*9*1*1*1*1*1*1*1*1*1*1*2*2*2*2*2*2*2*2*2*2*3 = 1114767360.
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CROSSREFS
| Cf. A000030, A000040, A001221, A001222, A112264, A112266-A112273.
Sequence in context: A071937 A061602 A033647 * A131451 A084012 A062919
Adjacent sequences: A109831 A109832 A109833 * A109835 A109836 A109837
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KEYWORD
| base,easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 31 2005
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