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a(1) = 2, a(2) = 3, a(n) = least prime greater than the product of two previous terms.
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%I #9 Aug 18 2019 01:45:17

%S 2,3,7,23,163,3761,613049,2305677323,1413493177187867,

%T 3259059164857285852640107,4606657893577361399569662402327877981883,

%U 15013370627425459052324121468319040208855976676229499210665181583

%N a(1) = 2, a(2) = 3, a(n) = least prime greater than the product of two previous terms.

%p a:=proc(n) if n=1 then 2 elif n=2 then 3 else nextprime(a(n-1)*a(n-2)) fi end: seq(a(n),n=1..13); # _Emeric Deutsch_, Feb 26 2005

%t nxt[{a_,b_}]:={b,NextPrime[a*b]}; Transpose[NestList[nxt,{2,3},15]] [[1]] (* _Harvey P. Dale_, Nov 24 2015 *)

%K nonn

%O 1,1

%A _Amarnath Murthy_, Nov 27 2003

%E More terms from _Emeric Deutsch_, Feb 26 2005