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%I #36 Jan 14 2024 09:01:01
%S 2,3,13,31,89,239,617,1571,4007,10141,25673,64853,163367,412007,
%T 1037759,2614369,6584857,16585291,41764859,105178831,264877933,
%U 667038311,1679809291,4230219377,10652786759,26826453991,67555877849
%N Smallest prime p such that Product_{primes q <= p} q+1 >= n*Product_{primes q <= p} q.
%C For k > 2, the primorial number A034386(A072997(k)) = A002110(A072986(k)) is the least unitary k-abundant number, i.e., the least number m such that usigma(m) >= k*m, where usigma(m) = A034448(m) is the sum of unitary divisors of m. The sequence of these primorials is the unitary version of A023199. - _Amiram Eldar_, Aug 24 2018
%F It seems that lim_{n -> oo} a(n+1)/a(n) exists and is > 2.
%F a(n) = A000040(A072986(n)). - _Amiram Eldar_, Aug 24 2018
%t n=x=y=1; Do[x *= (Prime[s] + 1); y *= Prime[s]; If[x >= n*y, Print[Prime[s]]; n++ ], {s, 1, 10^6}] (* _Ryan Propper_, Jul 22 2005 *)
%o (PARI) a(n)=if(n<0,0,s=1; while(prod(i=1,s, prime(i)+1)<prod(i=1,s, prime(i))*n,s++); prime(s));
%Y Cf. A072986.
%K hard,more,nonn
%O 1,1
%A _Benoit Cloitre_, Aug 14 2002
%E 7 more terms from _Ryan Propper_, Jul 22 2005
%E a(18)-a(22) added by _Amiram Eldar_, Aug 24 2018 from the data at A072986
%E a(23)-a(27) from _Keith F. Lynch_, Jan 13 2024
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