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A282027 a(n+1) = smallest prime p > a(n) such that p-1 divides a(1)*a(2)*...*a(n); or if no such prime p exists, then a(n+1) = smallest prime > a(n).

%I A282027 #15 Nov 22 2020 01:32:47
%S A282027 2,3,7,43,47,283,659,1319,1699,9227,11887,55399,71359,159707,396719,
%T A282027 558643,793439,794039,1117379,1117943,1143887,2235887,5554067,6707747,
%U A282027 6863323,13734803,15667447,16663963,18214099,20123239,45196799,46954223,55937239,93908447
%N A282027 a(n+1) = smallest prime p > a(n) such that p-1 divides a(1)*a(2)*...*a(n); or if no such prime p exists, then a(n+1) = smallest prime > a(n).
%H A282027 Jinyuan Wang, <a href="/A282027/b282027.txt">Table of n, a(n) for n = 1..200</a>
%p A282027 A[1]:= 2: P:= 1:
%p A282027 for n from 2 to 30 do
%p A282027   P:= A[n-1]*P;
%p A282027   p0:= nextprime(A[n-1]);
%p A282027   p:= p0;
%p A282027   while p-1 <= P and P mod (p-1) <> 0 do
%p A282027     p:= nextprime(p)
%p A282027   od:
%p A282027   if p-1 > P then A[n]:= p0
%p A282027   else A[n]:= p
%p A282027   fi;
%p A282027 od:
%p A282027 seq(A[i],i=1..30); # _Robert Israel_, Mar 17 2017
%o A282027 (PARI) lista(nn) = {my(d, k, m, t, v=List([2])); for(n=2, nn, k=1; m=oo; while((d=prod(i=1, t=k, v[i]))<m && k++<n, until(v[t]*d>m || t==n-1, t++); forsubset([t, k], w, if(ispseudoprime(d=prod(i=1, k, v[w[i]])+1) && d>v[n-1], m=min(m, d)))); listput(v, if(m<oo, m, nextprime(v[n-1]+1)))); v; } \\ _Jinyuan Wang_, Nov 21 2020
%Y A282027 Inspired by A007459 and A057459.
%K A282027 nonn
%O A282027 1,1
%A A282027 _N. J. A. Sloane_, Feb 13 2017
%E A282027 Corrected and extended by _Robert Israel_, Mar 17 2017
%E A282027 More terms from _Jinyuan Wang_, Nov 21 2020