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A060882 a(n) = n-th primorial (A002110) minus next prime.

%I A060882 #20 Feb 26 2023 02:23:11
%S A060882 -1,-1,1,23,199,2297,30013,510491,9699667,223092841,6469693199,
%T A060882 200560490093,7420738134769,304250263527167,13082761331669983,
%U A060882 614889782588491357,32589158477190044671,1922760350154212639009
%N A060882 a(n) = n-th primorial (A002110) minus next prime.
%C A060882 It is well-known and easy to prove (see Honsbeger) that a(n) > 0 for n > 1. - _N. J. A. Sloane_, Jul 05 2009
%C A060882 Terms are pairwise coprime with very high probability. I didn't find terms which are pairwise noncoprime, although it may be a case of the "strong law of small numbers." - _Daniel Forgues_, Apr 23 2012
%D A060882 R. Honsberger, Mathematical Diamonds, MAA, 2003, see p. 79. [Added by _N. J. A. Sloane_, Jul 05 2009]
%H A060882 Harry J. Smith, <a href="/A060882/b060882.txt">Table of n, a(n) for n = 0..100</a>
%H A060882 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha106.htm">P1 * Pn + NextPrime (n = 1 to 100)</a>
%H A060882 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha107.htm">P1 * Pn - NextPrime (n = 1 to 100)</a>
%H A060882 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha102.htm">P1 * Pn + 1 (n = 1 to 100)</a>
%H A060882 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">P1 * Pn - 1 (n = 1 to 100)</a>
%H A060882 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/index.htm">WIFC (World Integer Factorization Center)</a>
%p A060882 pp:=n->mul(ithprime(i),i=1..n);
%p A060882 [seq(pp(n)-ithprime(n+1),n=1..20)];
%t A060882 Join[{-1},With[{nn=20},#[[1]]-#[[2]]&/@Thread[{FoldList[Times,1, Prime[ Range[nn]]],Prime[Range[nn+1]]}]]] (* _Harvey P. Dale_, May 10 2013 *)
%o A060882 (PARI) { n=-1; m=1; forprime (p=2, prime(101), write("b060882.txt", n++, " ", m - p); m*=p; ) } \\ _Harry J. Smith_, Jul 13 2009
%o A060882 (Python)
%o A060882 from sympy import prime, primorial
%o A060882 def A060882(n): return primorial(n)-prime(n+1) if n else -1 # _Chai Wah Wu_, Feb 25 2023
%Y A060882 Cf. A002110, A060881, A064819, A006862, A057588.
%K A060882 sign
%O A060882 0,4
%A A060882 _N. J. A. Sloane_, May 05 2001