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A072236 Numbers of primes between successive primorials. 1
1, 2, 7, 36, 297, 2905, 39083, 603698, 11637502, 288086265, 7728273214, 251460107734, 9155428058351, 353182833587645, 15035130777416118 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sum of this series is pi(x).

LINKS

Table of n, a(n) for n=0..14.

Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x) [From Donovan Johnson, Apr 25 2010]

EXAMPLE

There are 3 primes less than 6, 7 primes between 6 and 30 and 36 primes between 30 and 210.

MATHEMATICA

Table[ PrimePi[ Product[Prime[i], {i, 1, n}]] - PrimePi[ Product[ Prime[i], {i, 1, n - 1}]], {n, 1, 12}]

Join[{1}, Differences[PrimePi/@Rest[FoldList[Times, 1, Prime[Range[12]]]]]] (* Harvey P. Dale, Mar 16 2012 *) (* Mathematica's implementation of PrimePi will not work for the 13th primorial because it's too large *)

CROSSREFS

Cf. A002110 & A000849.

Sequence in context: A012712 A012363 A012717 * A007474 A002724 A292206

Adjacent sequences:  A072233 A072234 A072235 * A072237 A072238 A072239

KEYWORD

hard,nonn

AUTHOR

Stephan Wagler (stephanwagler(AT)aol.com), Jul 05 2002

EXTENSIONS

Edited by Robert G. Wilson v, Jul 08 2002

a(13)-a(14) from Donovan Johnson, Apr 25 2010

STATUS

approved

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Last modified January 28 03:49 EST 2020. Contains 331317 sequences. (Running on oeis4.)