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a(1) = 2. For n > 1, a(n) is the least prime > a(n-1)*n/2.
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%I #16 Feb 05 2020 14:35:03

%S 2,3,5,11,29,89,313,1259,5669,28349,155921,935531,6080957,42566731,

%T 319250501,2554004029,21709034261,195381308371,1856122429537,

%U 18561224295377,194892855101467,2143821406116139,24653946170335607,295847354044027363,3698091925550342059,48075195032154446803

%N a(1) = 2. For n > 1, a(n) is the least prime > a(n-1)*n/2.

%t nxt[{n_,a_}]:={n+1,NextPrime[a (n+1)/2]}; NestList[nxt,{1,2},30][[All,2]] (* _Harvey P. Dale_, Feb 05 2020 *)

%o (PARI) lista(nn) = {my(a=2); print1(a, ", "); for (n=2, nn, if (a*n % 2, a = nextprime(a*n/2), a = nextprime(a*n/2+1)); print1(a, ", "););} \\ _Michel Marcus_, Sep 15 2019

%K nonn

%O 1,1

%A _Pierre CAMI_, May 08 2011

%E More terms from _Michel Marcus_, Sep 15 2019

%E Name edited by _Felix Fröhlich_, Sep 15 2019