|
%I #31 Aug 26 2021 21:32:42
%S 7,17,29,31,43,59,71,73,97,101,223,233,257,439,503,709,859,863,1013
%N Primes p such that p#-1 is a semiprime, where # is the primorial (A034386).
%C 1153 and 1381 are also terms. - _Amiram Eldar_, Feb 16 2020
%C a(20) >= 1091. 1091# - 1 is a 458-digit composite with no known factors. - _Hugo Pfoertner_, Feb 05 2021
%H FactorDB <a href="http://factordb.com/index.php?query=1013%23-1">Factorization of 1013#-1</a>.
%H FactorDB <a href="http://factordb.com/index.php?query=1091%23-1">Status of 1091#-1</a>.
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>, PI Pn - 1 (n = 1 to 110) (2013).
%F A001221(A034386(a(n)) - 1) = 2. - _Amiram Eldar_, Feb 16 2020
%e a(2) = 17 so 17# - 1 = 510509 = 61 * 8369 is a semiprime.
%t p = Select[Range[101], PrimeQ]; p[[ Position[FoldList[Times, p] - 1, _?(PrimeOmega[#] == 2 &)] //Flatten ]] (* _Amiram Eldar_, Feb 16 2020 *)
%Y Cf. A001221, A001358, A002110, A006794, A034386, A057588, A078781, A250293.
%K nonn,hard,more
%O 1,1
%A _Eric Chen_, Dec 24 2014
%E a(15)-a(18) using factordb.com from _Amiram Eldar_, Feb 16 2020
%E a(19) using factordb.com from _Hugo Pfoertner_, Feb 05 2021
%E Edited by _Max Alekseyev_, Aug 26 2021
|
