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Search: id:A058033
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| A058033 |
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Number of powers of 2 between (but not including) two consecutive primorials. |
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+0
5
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| 1, 2, 3, 4, 3, 4, 5, 4, 5, 5, 5, 6, 5, 6, 5, 6, 6, 6, 6, 7, 6, 6, 7, 6, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 8, 7, 8, 7, 8, 7, 8, 8, 7, 8, 8, 8, 8, 7, 8, 8, 8, 8, 8, 9, 8, 8, 8, 8, 8, 9, 8, 8, 9, 8, 9, 8, 8, 9, 8, 9, 9, 8, 9, 8, 9, 9, 8, 9, 9, 9, 8, 9, 9, 9, 9, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 9, 9, 9
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Does not increase monotonically.
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FORMULA
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a(n)= Cardinality{b |A002110(n)<= b < A002110(n+1), b=2^x for some x} a(n)=A045716(n+1)-A045716(n)
First differences of A054850.
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EXAMPLE
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Between [2 and 6] is 4, between [6 and 30] are 8, 16, between [30 and
210] are 32, 64, 128 and between [210 and 2310] are 256, 512, 1024, 2048, between [2310
and 30030] are 4096, 8192, 16384 between [30030, 510510] are
32768, 65536, 131072, 262144. So a(1), ..., a(6)=1, 2, 3, 4, 3, 4, ...
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MATHEMATICA
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a = Table[ Floor[ Log[2, Product[ Prime[i], {i, 1, n}]]], {n, 1, 110}]; Drop[a, 1] - Drop[a, -1]
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CROSSREFS
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Cf. A002110, A045716, A054850, A084972.
Sequence in context: A030563 A081399 A114524 this_sequence A125619 A123066 A081748
Adjacent sequences: A058030 A058031 A058032 this_sequence A058034 A058035 A058036
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 22 2000
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), May 22 2003
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