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%I #19 Jan 20 2024 17:10:16
%S 2,3,7,8,14,16,18,20,40,42,44,53,134,154,185,187,191,197,200,201,230,
%T 235,239,244,256,282,303,358,489,536,665,684,719,1098,1204,1400,1516,
%U 1629,1903,1997,1999,2104,2477,3075,3676,3785,4115,5429,5808,6069,6276,9095
%N Numbers k such that k#*2^k-1 is prime, where k# = product of primes <= k.
%C The values corresponding to terms 1098 through 1516 have been proved to be prime.
%C No more terms < 10000. - _L. Joris Perrenet_, Mar 18 2020
%H The OpenPFGW Project, <a href="http://www.primeform.net/openpfgw/">Primality Tester</a>.
%t p = 1; Do[If[PrimeQ[n], p *= n]; If[PrimeQ[p*2^n - 1], Print[n]], {n, 2, 10000}] (* _Ryan Propper_, Sep 05 2005 *)
%t Select[Table[{k,Times@@Prime[Range[PrimePi[k]]]},{k,720}],PrimeQ[#[[2]]2^#[[1]]-1]&][[;;,1]] (* The program generates the first 33 terms of the sequence. *) (* _Harvey P. Dale_, Jan 20 2024 *)
%Y Cf. A034386.
%K nonn
%O 1,1
%A _Jason Earls_, Jun 24 2003
%E More terms from _Ryan Propper_, Sep 05 2005
%E a(52) from _L. Joris Perrenet_, Mar 18 2020
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