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A084320 Number of powers of two between 2 consecutive factorials (2! including). 3
1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 6, 5, 5, 6, 5, 6, 5, 6, 5, 6, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 6, 6, 6, 5, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 6, 6, 7, 6, 6, 7, 6, 7, 6, 7, 6, 6, 7, 7, 6, 7, 6, 7, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A067850(n+1) - A067850(n).

a(n) = A000523(n) + O(1). - Charles R Greathouse IV, Dec 26 2013

EXAMPLE

n=7: a(7)=3 because between 5040 and 40320 three powers of 2 occur: 8192, 16384 and 32768.

MATHEMATICA

Table[Floor[Log[2, (w+1)! ]//N]-Floor[Log[2, w! ]//N], {w, 1, 128}]

PROG

(PARI) a(n)=if(n<6, (n+1)\2, log((n+1)!)\log(2)-log(n!)\log(2)) \\ Charles R Greathouse IV, Dec 26 2013

CROSSREFS

Cf. A067850, A058033, A000142, A000079.

Sequence in context: A105047 A089881 A251547 * A161358 A120699 A072643

Adjacent sequences:  A084317 A084318 A084319 * A084321 A084322 A084323

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 19 2003

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)