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A008952
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Leading digit of 2^n.
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4
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1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, 2, 4, 8, 1, 3, 7, 1, 2, 5, 1, 2, 4, 9, 1, 3, 7, 1, 2, 5, 1, 2, 4, 9, 1, 3, 7, 1, 2, 5, 1, 2, 4, 9, 1, 3, 7, 1, 3, 6, 1, 2, 4, 9, 1, 3, 7, 1, 3, 6, 1, 2, 4, 9, 1, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Statistically, sequence obeys Benford's law, i.e. digit d occurs with probability log_10(1 + 1/d); thus 1 appears about 6.6 times more often than 9. - Lekraj Beedassy (blekraj(AT)yahoo.com), May 04 2005
The most significant digits of the n-th powers of 2 are not cyclic and in the first 1000000 terms, 1 appears 301030 times, 2 appears 176093, 3 appears 124937, 4 appears 96911, 5 appears 79182, 6 appears 66947, 7 appears 57990, 8 appears 51154 and 9 appears 45756 times. - Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 03 2008
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LINKS
| Robert G. Wilson v, Table of n, a(n) for n = 0..100000.
J. Derbyshire, Lead Digit of 2 to the Power of N
Wikipedia, Frank Benford's law.
Wikipedia, George Zipf's law.
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FORMULA
| a(n) = [2^n / 10^([log_10(2^n)])] = [2^n / 10^([n*log_10(2)])]
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MATHEMATICA
| f[n_] := First@ IntegerDigits[2^n] = Quotient[2^n, 10^Floor[n*Log[10, 2]]]; Table[ f@n, {n, 0, 104}] (* Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 03 2008 *)
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CROSSREFS
| Cf. A000030.
Sequence in context: A072032 A023104 A133145 * A021407 A131609 A100880
Adjacent sequences: A008949 A008950 A008951 * A008953 A008954 A008955
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KEYWORD
| nonn,base
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AUTHOR
| Leonid Broukhis
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