A165768 -id:A165768 - cp's OEIS frontend

A085745 Numbers m such that 2^m + m is a semiprime.

2, 11, 23, 34, 59, 69, 87, 95, 119, 123, 129, 171, 197, 239, 341, 425, 455, 471, 515, 519, 635, 765, 959, 1115, 1181, 1210

Offset: 1

Jason Earls, Jul 21 2003

a(27) >= 1239. If 1239 is not a term then a(27) = 1275. - Amiram Eldar, Oct 26 2024

factordb, 2^1239+1239.

Cf. A006127, A052007, A089535, A089536, A089537.

Sequences A165767, A165768, A165769 are the analog for 2^n-n. - M. F. Hasler, Oct 08 2009

Select[Range[1300],PrimeOmega[2^#+#]==2&] (* Harvey P. Dale, Dec 18 2014 *)

a(n) = 2*k <=> A089535(n) is even <=> A089536(n) = 2 <=> A089537(n) = 4^k/2 + k, and for any prime of this form, there is a term a(n) = 2*k in this sequence. - M. F. Hasler, Oct 08 2009

More terms from Ray Chandler, Nov 08 2003
a(15) from Donovan Johnson, Mar 06 2008
a(16)-a(26) from Sean A. Irvine, Oct 27 2009
Offset changed to 1 by Jinyuan Wang, Jul 30 2021

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

Original entry on oeis.org

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

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

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

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

Cf. A080892, A081715

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

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

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

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

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

A165769 Largest prime factor of the semiprime 2^A165767(n)-A165767(n).

Original entry on oeis.org

29, 11, 4679, 131063, 123817, 318949, 209510599, 49977801259, 2199023255531, 9334079, 7250118529, 2305843009213693921, 17457916757373919459, 27748320404471, 717308900550128276543, 2028240960365167042394725128581, 221537999297485978817301176713390723

Offset: 1

M. F. Hasler, Oct 08 2009

nonn

A165768(n)=2 <=> A165767(n)=2k for some k <=> a(n)=4^k/2-k is prime. This is the case for k=3,9,21,31,1125,...

			46235097144973199564251065756966919577339221 is in this sequence because it is the largest prime factor of the semiprime 2^199-199.

Max Alekseyev, Table of n, a(n) for n = 1..39

a(n)=(2^A165767(n)-A165767(n))/A165768(n).

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A085745 Numbers m such that 2^m + m is a semiprime.

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

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A165769 Largest prime factor of the semiprime 2^A165767(n)-A165767(n).

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