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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.)