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

4, 6, 10, 25, 28, 32, 98, 124, 146, 164, 182, 190, 200, 220, 226, 230, 248, 280, 362, 376, 418, 446, 518, 544

Offset

1,1

Comments

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

No more odd terms after a(4) = 25 for m < 200000. a(25) >= 626. - Hugo Pfoertner, Aug 07 2019

Links

Table of n, a(n) for n=1..24.

factordb.com, Status of 3^626-626.

Example

4 is in this sequence because 3^4 - 4 = 7*11 is semiprime.
10 is in this sequence because 3^10 - 10 = 43*1373 and these two factors are prime.

Maple

select(n -> numtheory:-bigomega(3^n - n) = 2, [$1..150]); # Robert Israel, Jan 02 2015

Mathematica

Select[Range[150], PrimeOmega[3^# - #] == 2 &]

Prog

(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];
(PARI) is(m) = bigomega(3^m-m)==2 \\ Felix Fröhlich, Dec 30 2014
(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

Crossrefs

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).

Cf. A001358 (semiprimes), A058037, A252788.

Sequence in context: A277343 A077065 A131867 * A322961 A291542 A242565

Adjacent sequences: A252653 A252654 A252655 * A252657 A252658 A252659

Keyword

nonn,more,hard

Author

Vincenzo Librandi, Dec 20 2014

Extensions

a(10) from Felix Fröhlich, Dec 30 2014

a(11)-a(14) from Charles R Greathouse IV, Jan 02 2015

a(15)-a(24) from Luke March, Aug 21 2015

Status

approved