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First differences of sequence of primorials.
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%I #18 Feb 23 2022 12:24:33

%S 1,4,24,180,2100,27720,480480,9189180,213393180,6246600360,

%T 194090796900,7220177644680,296829525392400,12778511068142820,

%U 601807021256821380,31974268694601553320,1890171191677022594340,115365621009252758344200,7741033169720860084895820

%N First differences of sequence of primorials.

%C Largest number below primorial(n + 1) to be divisible by the first n primes. - _Alonso del Arte_, Dec 13 2014

%H Harry J. Smith, <a href="/A061720/b061720.txt">Table of n, a(n) for n=0..100</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

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

%e a(2) = primorial(3) - primorial(2) = 30 - 6 = 24.

%e a(3) = primorial(4) - primorial(3) = 210 - 30 = 180.

%p p:= proc(n) option remember; `if`(n=0, 1, ithprime(n)*p(n-1)) end:

%p a:= n-> p(n+1)-p(n):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Feb 23 2022

%t Differences[FoldList[Times, 1, Prime[Range[20]]]] (* _Alonso del Arte_, Dec 13 2014 *)

%o (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

%Y Cf. A002110, A006093, A286629.

%Y Subsequence of A276155.

%K easy,nonn

%O 0,2

%A _Labos Elemer_, Jun 20 2001

%E Since primorial(0) = 1, term a(0) = 1 added by _Harry J. Smith_, Jul 27 2009