A250293 - OEIS

%I #38 May 08 2023 02:08:23

%S 13,19,23,43,61,67,73,83,101,139,151,173,223,251,383,457,571,673,761

%N Primes p such that p#+1 is a semiprime, where # is the primorial (A034386).

%C The next candidate after 571 is 859. 859# + 1 is a 359-digit composite with no known factors. - _Hugo Pfoertner_, Feb 05 2021

%H factordb.com, <a href="http://factordb.com/index.php?query=859%23%2B1">Status of 859#+1</a>.

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha102.htm">Factorizations of many number sequences</a>, PI Pn + 1 (n = 1 to 110) (2012).

%F a(n) = prime(A085725(n)). - _Hugo Pfoertner_, Feb 05 2021

%e a(1) = 13 so 13# + 1 = 30031 = 59 * 509 is a semiprime.

%t Prime[#]&/@(Module[{pmrl=FoldList[Times,Prime[Range[50]]]},Position[ pmrl, _?(PrimeOmega[ #+1]==2&)]]//Flatten) (* _Harvey P. Dale_, Apr 29 2017 *)

%Y Cf. A005234, A006862, A034386, A078778, A085725, A250294.

%K nonn,hard,more

%O 1,1

%A _Eric Chen_, Dec 24 2014

%E a(16)-a(18) using factordb.com from _Hugo Pfoertner_, Feb 05 2021

%E Missing 571 inserted by _Sean A. Irvine_, Mar 03 2023