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A067497
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Smallest k for which 2^k is n+1 decimal digits long, and equivalently numbers k such that 1 is the first digit of 2^k.
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15
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0, 4, 7, 10, 14, 17, 20, 24, 27, 30, 34, 37, 40, 44, 47, 50, 54, 57, 60, 64, 67, 70, 74, 77, 80, 84, 87, 90, 94, 97, 100, 103, 107, 110, 113, 117, 120, 123, 127, 130, 133, 137, 140, 143, 147, 150, 153, 157, 160, 163, 167, 170, 173, 177, 180, 183, 187, 190, 193, 196
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OFFSET
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0,2
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COMMENTS
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The asymptotic density of this sequence is log_10(2) = 0.301029... (A007524). - Amiram Eldar, Jan 27 2021
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LINKS
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FORMULA
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MATHEMATICA
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a[n_] := Block[{k = 0}, While[ Floor[Log[10, 2^k] + 1] < n, k++ ]; k]; Table[ a[n], {n, 1, 61}]
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PROG
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(PARI) for(n=0, 500, if(floor(2^n/10^(floor(n*log(2)/log(10))))==1, print1(n, ", ")))
(PARI) a(n) = ceil(n*log(10)/log(2)); \\ Michel Marcus, May 13 2017
(GAP) Filtered([0..200], n->ListOfDigits(2^n)[1]=1); # Muniru A Asiru, Oct 22 2018
(Python)
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CROSSREFS
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KEYWORD
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base,nonn,easy
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AUTHOR
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EXTENSIONS
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Additional comments from Lekraj Beedassy, Jun 20 2002 and from Rick Shephard, Jun 27 2002
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STATUS
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approved
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