A061720 First differences of sequence of primorials.

1, 4, 24, 180, 2100, 27720, 480480, 9189180, 213393180, 6246600360, 194090796900, 7220177644680, 296829525392400, 12778511068142820, 601807021256821380, 31974268694601553320, 1890171191677022594340, 115365621009252758344200, 7741033169720860084895820

Offset

0,2

Comments

Largest number below primorial(n + 1) to be divisible by the first n primes. - Alonso del Arte, Dec 13 2014

Links

Harry J. Smith, Table of n, a(n) for n=0..100

Index entries for sequences related to primorial numbers

Formula

a(n) = A002110(n+1) - A002110(n) = A002110(n)*A006093(n+1).

Example

a(2) = primorial(3) - primorial(2) = 30 - 6 = 24.
a(3) = primorial(4) - primorial(3) = 210 - 30 = 180.

Maple

p:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*p(n-1)) end:
a:= n-> p(n+1)-p(n):
seq(a(n), n=0..20);  # Alois P. Heinz, Feb 23 2022

Mathematica

Differences[FoldList[Times, 1, Prime[Range[20]]]] (* Alonso del Arte, Dec 13 2014 *)

Prog

(PARI) { n=-1; r=q=1; forprime (p=2, prime(101), r*=p; write("b061720.txt", n++, " ", r-q); q=r ) } \\ Harry J. Smith, Jul 27 2009

Crossrefs

Cf. A002110, A006093, A286629.

Subsequence of A276155.

Sequence in context: A309637 A168452 A361594 * A197472 A152403 A111556

Adjacent sequences: A061717 A061718 A061719 * A061721 A061722 A061723

Keyword

easy,nonn

Author

Labos Elemer, Jun 20 2001

Extensions

Since primorial(0) = 1, term a(0) = 1 added by Harry J. Smith, Jul 27 2009

Status

approved