A242274 Numbers k such that k*3^k - 1 is semiprime.

4, 5, 8, 12, 20, 24, 25, 28, 32, 38, 42, 44, 60, 62, 66, 70, 72, 80, 122, 125, 148, 228, 244, 270, 389, 390, 432, 464, 470, 488, 549, 560, 804, 862

Offset

1,1

Comments

The semiprimes of this form are 323, 1214, 52487, 6377291, 69735688019, 6778308875543, 21182215236074, 640550188738907, 59296646043258911, ...

804 is a term of this sequence. - Luke March, Aug 22 2015

The smallest unresolved value of k is now 862. - Sean A. Irvine, Jun 20 2022

The smallest unresolved value of k is now 866. - Tyler Busby, Oct 06 2023

From Jon E. Schoenfield, Oct 06 2023: (Start)

After the possible term 866, the only remaining 3-digit terms are 912 and 984, unless 920 is a term.

If k is an odd term, then k*3^k - 1 is even, so (k*3^k - 1)/2 is a prime. The next odd terms after 549 are 1125 and 12889. Odd terms are in A366323. (End)

Links

Table of n, a(n) for n=1..34.

Mathematica

Select[Range[241], PrimeOmega[# 3^# - 1]==2&]

Prog

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..241] | IsSemiprime(s) where s is n*3^n-1];
(PARI) isok(n)=bigomega(n*3^n-1)==2 /* Anders Hellström, Aug 18 2015 */

Crossrefs

Cf. similar sequence listed in A242273.

Cf. A006553, A060352, A366323.

Sequence in context: A260163 A362560 A061765 * A297419 A230549 A133940

Adjacent sequences: A242271 A242272 A242273 * A242275 A242276 A242277

Keyword

nonn,more

Author

Vincenzo Librandi, May 12 2014

Extensions

a(21)-a(23) from Carl Schildkraut, Aug 18 2015

a(24)-a(32) from Luke March, Aug 22 2015

a(32) = 804 removed by Sean A. Irvine, Apr 25 2022

a(32)-a(33) from Sean A. Irvine, Jun 20 2022

a(34) from Tyler Busby, Oct 06 2023

Status

approved