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 A058033 Number of powers of 2 between (but not including) two consecutive primorials. 5
 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; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Does not increase monotonically. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 FORMULA 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. EXAMPLE Between [2 and 6] is 4; between [6 and 30] are 8, 16; between [30 and 210] are 32, 64, 128; 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, ... From Michael De Vlieger, Jul 15 2017: (Start) First and last positions of values seen in the first 10^5 terms: Value  First   Last    1      1       1    2      2       2    3      3       5    4      4       8    5      7      15    6     12      27    7     20      51    8     35      90    9     57     161   10    102     294   11    182     542   12    323     995   13    585    1856   14   1061    3505   15   1943    6485   16   3521   12203   17   6606   22949   18  12297   43200   19  23051   81759   20  43578  (99999)   21  82296  (99997) (End) MATHEMATICA a = Table[ Floor[ Log[2, Product[ Prime[i], {i, 1, n}]]], {n, 1, 110}]; Drop[a, 1] - Drop[a, -1] (* Second program: *) Differences@ Floor@ Log2@ FoldList[Times, Prime@ Range@ 105] (* Michael De Vlieger, Jul 15 2017 *) CROSSREFS Cf. A002110, A045716, A054850, A084972. Sequence in context: A205554 A214613 A114524 * A216197 A307531 A125619 Adjacent sequences:  A058030 A058031 A058032 * A058034 A058035 A058036 KEYWORD nonn AUTHOR Labos Elemer, Nov 22 2000 EXTENSIONS Edited by Robert G. Wilson v, May 22 2003 STATUS approved

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Last modified August 24 22:41 EDT 2019. Contains 326314 sequences. (Running on oeis4.)