A072236 Numbers of primes between successive primorials.

1, 2, 7, 36, 297, 2905, 39083, 603698, 11637502, 288086265, 7728273214, 251460107734, 9155428058351, 353182833587645, 15035130777416118

Offset

0,2

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 A348106

Adjacent sequences: A072233 A072234 A072235 * A072237 A072238 A072239

Keyword

nonn,hard,more

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