cp's OEIS Frontend

A252656 Numbers n such that 3^n - n is a semiprime.

%I A252656 #38 Sep 08 2022 08:46:10
%S A252656 4,6,10,25,28,32,98,124,146,164,182,190,200,220,226,230,248,280,362,
%T A252656 376,418,446,518,544
%N A252656 Numbers n such that 3^n - n is a semiprime.
%C A252656 Are there odd members of the sequence other than 25?  There are no others < 10000.  An odd number m is in the sequence iff (3^m - m)/2 is prime. - _Robert Israel_, Jan 02 2015
%C A252656 No more odd terms after a(4) = 25 for m < 200000. a(25) >= 626. - _Hugo Pfoertner_, Aug 07 2019
%H A252656 factordb.com, <a href="http://factordb.com/index.php?query=3%5E626-626">Status of 3^626-626</a>.
%e A252656 4 is in this sequence because 3^4 - 4 = 7*11 is semiprime.
%e A252656 10 is in this sequence because 3^10 - 10 = 43*1373 and these two factors are prime.
%p A252656 select(n -> numtheory:-bigomega(3^n - n) = 2, [$1..150]); # _Robert Israel_, Jan 02 2015
%t A252656 Select[Range[150], PrimeOmega[3^# - #] == 2 &]
%o A252656 (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [m: m in [2..150] | IsSemiprime(s) where s is 3^m-m];
%o A252656 (PARI) is(m) = bigomega(3^m-m)==2 \\ _Felix Fröhlich_, Dec 30 2014
%o A252656 (PARI) n=1;while(n<100,s=3^n-n;c=0;forprime(p=1,10^4,if(s%p,c++);if(s%p==0,s1=s/p;if(ispseudoprime(s1),print1(n,", ");c=0;break);if(!ispseudoprime(s1),c=0;break)));if(!c,n++);if(c,if(bigomega(s)==2,print1(n,", "));n++)) \\ _Derek Orr_, Jan 02 2015
%Y A252656 Cf. numbers m such that k^m - m is a semiprime: A165767 (k = 2), this sequence (k = 3), A252657 (k = 4), A252658 (k = 5), A252659 (k = 6), A252660 (k = 7), A252661 (k = 8), A252662 (k = 9), A252663 (k = 10).
%Y A252656 Cf. A001358 (semiprimes), A058037, A252788.
%K A252656 nonn,more,hard
%O A252656 1,1
%A A252656 _Vincenzo Librandi_, Dec 20 2014
%E A252656 a(10) from _Felix Fröhlich_, Dec 30 2014
%E A252656 a(11)-a(14) from _Charles R Greathouse IV_, Jan 02 2015
%E A252656 a(15)-a(24) from _Luke March_, Aug 21 2015