A072236 Numbers of primes between successive primorials.

1, 2, 7, 36, 297, 2905, 39083, 603698, 11637502, 288086265, 7728273214, 251460107734, 9155428058351, 353182833587645, 15035130777416118, 726840450530910033, 39326730322451969003, 2211193504550790268932, 137315317472893091758587

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

Formula

a(n) = A000849(n+1) - A000849(n). - Amiram Eldar, Jun 11 2024

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

a(15)-a(18) calculated using the data at A000849 and added by Amiram Eldar, Jun 11 2024

Status

approved