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A137284
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a(0)=1 and a(n) for n > 0 equals the minimal positive integer such that addition of 2^(-a(n)) to Sum_{k = 0,1,...,n-1} 2^(-a(k)) changes only trailing zeros in its decimal representation.
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2
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1, 4, 14, 47, 157, 522, 1735, 5764, 19148, 63609, 211305, 701941, 2331798, 7746066, 25731875, 85479439, 283956550, 943283242, 3133519104, 10409325148, 34579029658, 114869050115, 381586724811, 1267603661786, 4210888217270, 13988267873380, 46468020047392
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OFFSET
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0,2
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COMMENTS
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First and last nonzero decimal digits of 2^(-m) appear respectively at the ceiling(m/log_2(10))-th and m-th positions after the point. Hence a(n+1) equals the minimum solution to ceiling(x/log_2(10)) = a(n) + 1, which is x = ceiling(a(n)*log_2(10)).
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LINKS
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FORMULA
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EXAMPLE
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Start from 0;
0 + 2^(-1) = 0.5;
0.5 + 2^(-4) = 0.5625 (first digit "5" is equal to the decimal of previous number);
0.5625 + 2^(-14) = 0.56256103515625 (first digits "5625" are equal to the decimals of previous number);
etc.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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