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Search: id:A111497
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| A111497 |
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Difference between successive terms of floor(10^n/Li(10^n) - 1). |
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+0
1
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| 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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10^n/Li(10^n) - 1) is the ratio of estimated composite numbers less than 10^n to the estimated prime numbers less than 10^n. Conjecture: 2 and 3 are the only numbers in this sequence.
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FORMULA
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Li(n) is the logarithmic integral which approximates the number of primes less than n. n Li(n) = Int dt/log(t) 2
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PROGRAM
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(PARI) LiRatioDiff(m, n) = { local(x, p1, p2, a, b); forstep(x=m, n, 2, p1=10.^x; p2=10^(x+1); a=floor(p1/Li(p1)-1); b=floor(p2/Li(p2)-1); print1(b-a, ", ") ) } Li(x) = \ Logarithmic integral { -eint1(log(1/x)) }
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CROSSREFS
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Sequence in context: A120881 A031217 A078545 this_sequence A097051 A078832 A086410
Adjacent sequences: A111494 A111495 A111496 this_sequence A111498 A111499 A111500
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Nov 16 2005
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