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Search: id:A092097
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| A092097 |
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Limit number of (m-n)-almost-primes in range [2^m..2^{m+1}-1]. |
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+0
4
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| 2, 5, 8, 22, 47, 103, 234, 493, 1087, 2282, 4901, 10427, 21993, 46389, 97394, 204567, 427099, 892587, 1858338, 3865692, 8027140, 16642918, 34463760, 71273199, 147235636, 303814862, 626313383, 1289883519, 2654196000
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Also number of odd numbers k for which floor(log_2(k)) - bigomega(k) = n, where bigomega is A001222. Frank Adams-Watters Jun 20 2006
The value of m at which the number of (m-n)-almost-primes reaches its limit is floor(n/(log_2(3)-1))+n-1: 1,4,7,9,12,15,17,20,23,26,28; not A026356: 2,4,7,9,12,15,17,20,22,25,28 as originally conjectured. Frank Adams-Watters Jun 20 2006
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FORMULA
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For n>0, a(n) = A052130(n+1)-A052130(n).
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EXAMPLE
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a(0) = 2: m-almost primes in [2^m..2^{m+1}-1] are 2^m and
3*2^{m-1}. a(1) = 5; (m-1)-almost-primes in [2^m..2^{m-1}] are
5*2^{m-2}, 7*2^{m-2}, 9*2^{m-3}, 15*2^{m-3} and 27*2^{m-4}.
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CROSSREFS
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Cf. A052130, A001222, A026356, A120033-A120043.
Sequence in context: A001005 A009735 A137095 this_sequence A088144 A100501 A142869
Adjacent sequences: A092094 A092095 A092096 this_sequence A092098 A092099 A092100
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KEYWORD
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easy,nonn
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AUTHOR
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Andrew Plewe (aplewe(AT)sbcglobal.net), Feb 19 2004
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EXTENSIONS
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Edited and extended by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 20 2006
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