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

6, 7, 15, 18, 25, 31, 33, 39, 42, 45, 49, 62, 73, 85, 93, 103, 119, 171, 187, 193, 199, 201, 269, 367, 379, 405, 413, 449, 459, 481, 489, 549, 577, 601, 631, 669, 787, 795, 1399

Offset: 1

Author

M. F. Hasler, Oct 08 2009, Oct 29 2009

Keywords

• nonn
• more
• hard

Comments

The largest resp. smallest prime factor of 2^a(n)-a(n) is listed in A165768 resp. A165769.

a(40) >= 1489. - Max Alekseyev, Aug 05 2019

1501, 1587, 1667, 2250, 3393, 5845, 9967, 16147 are terms of this sequence. - Chai Wah Wu, Oct 18 2019

Examples

			199 is in this sequence because 2^199-199 = 17377902756647509 * 46235097144973199564251065756966919577339221 and these two factors are prime.
		

Crossrefs

Cf. A080892, A081715

Programs

Mathematica

Select[Range[1000], PrimeOmega[2^# - #]==2 &] (* Vincenzo Librandi, Dec 19 2014 *)

PARI

for( i=1,200, bigomega(2^i-i)==2 & print1(i","))

Formula

2^a(n)-a(n) = A165768(n)*A165769(n) is a semiprime.

a(n)=2k <=> 4^k/2-k is prime <=> A165768(n)=2.

Extensions

More terms from Sean A. Irvine, Oct 22 2009

a(36)-a(37) from Max Alekseyev, Jun 06 2013

a(38) from Sean A. Irvine, Mar 17 2015

a(39) from Sean A. Irvine, Jun 29 2015