cp's OEIS Frontend

A165767 Numbers m such that 2^m-m is a semiprime.

%I A165767 #34 Oct 19 2019 03:34:19
%S A165767 6,7,15,18,25,31,33,39,42,45,49,62,73,85,93,103,119,171,187,193,199,
%T A165767 201,269,367,379,405,413,449,459,481,489,549,577,601,631,669,787,795,
%U A165767 1399
%N A165767 Numbers m such that 2^m-m is a semiprime.
%C A165767 The largest resp. smallest prime factor of 2^a(n)-a(n) is listed in A165768 resp. A165769.
%C A165767 a(40) >= 1489. - _Max Alekseyev_, Aug 05 2019
%C A165767 1501, 1587, 1667, 2250, 3393, 5845, 9967, 16147 are terms of this sequence. - _Chai Wah Wu_, Oct 18 2019
%F A165767 2^a(n)-a(n) = A165768(n)*A165769(n) is a semiprime.
%F A165767 a(n)=2k <=> 4^k/2-k is prime <=> A165768(n)=2.
%e A165767 199 is in this sequence because 2^199-199 = 17377902756647509 * 46235097144973199564251065756966919577339221 and these two factors are prime.
%t A165767 Select[Range[1000], PrimeOmega[2^# - #]==2 &] (* _Vincenzo Librandi_, Dec 19 2014 *)
%o A165767 (PARI) for( i=1,200, bigomega(2^i-i)==2 & print1(i","))
%Y A165767 Cf. A080892, A081715
%K A165767 nonn,more,hard
%O A165767 1,1
%A A165767 _M. F. Hasler_, Oct 08 2009, Oct 29 2009
%E A165767 More terms from _Sean A. Irvine_, Oct 22 2009
%E A165767 a(36)-a(37) from _Max Alekseyev_, Jun 06 2013
%E A165767 a(38) from _Sean A. Irvine_, Mar 17 2015
%E A165767 a(39) from _Sean A. Irvine_, Jun 29 2015