A099442 -id:A099442 - cp's OEIS frontend

A099439 Numbers k such that A000295(k) = 2^k-k-1 is prime.

4, 10, 14, 16, 26, 50, 56, 70, 116, 2072, 6250, 13670, 14216, 14626, 396128

Offset: 1

Hugo Pfoertner, Oct 18 2004

The next term is > 400000.
Equals A063791 + 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Some of the results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

			a(1) = 4 because 2^4 - 4 - 1 = 11 is prime.

Cf. A000295 (2^n-n-1), A099440 (primes in A000295), A099441 (2^n-n-1 is a semiprime), A099442 (semiprimes in A000295).

a(15) (a PRP) from Karsten Bonath, Jun 07 2018

A099440 Primes of the form A000295(k) = 2^k - k - 1.

Original entry on oeis.org

11, 1013, 16369, 65519, 67108837, 1125899906842573, 72057594037927879, 1180591620717411303353, 83076749736557242056487941267521419

Offset: 1

Hugo Pfoertner, Oct 18 2004

nonn

The next term a(10) = 2^2072-2073 has 624 decimal digits.

a(11) has 1882 decimal digits. - Vincenzo Librandi, Jul 18 2012

			a(2) = 1013 because A000295(A099439(2)) = 2^10 - 10 - 1 is prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..10

Cf. A000295 2^n-n-1 (column 2 of the Eulerian numbers), A099439 2^n-n-1 is prime, A099441 2^n-n-1 is a semiprime, A099442 semiprimes in A000295.

[ a: n in [1..200] | IsPrime(a) where a is 2^n-n-1 ]; // Vincenzo Librandi, Jul 18 2012

Select[Table[2^n-n-1,{n,0,7000}],PrimeQ] (* Vincenzo Librandi, Jul 18 2012 *)

A099441 Numbers n such that A000295(n) = 2^n-n-1 is a semiprime.

Original entry on oeis.org

3, 5, 6, 8, 9, 12, 30, 32, 33, 46, 52, 62, 74, 76, 86, 98, 130, 134, 154, 228, 230, 242, 256, 266, 346, 352, 382, 412, 428, 474, 488, 634, 650, 662, 688, 704, 722, 772, 896, 986, 1108, 1222, 1246, 1326

Offset: 1

Hugo Pfoertner, Oct 18 2004

A candidate for the next term is a(45) = 1736. 2^1736-1737 is composite with 523 decimal digits and unknown factorization. - Tyler Busby, Jan 05 2025

			a(3) = 6 because 2^6-6-1 = 57 = 3*19 is a semiprime.

Dario Alpern, Factorization using the Elliptic Curve Method.
Status of 2^1736-1737 in factordb.com.

Cf. A000295 (2^n-n-1 (column 2 of the Eulerian numbers)), A099439 (2^n-n-1 is prime), A099440 (primes in A000295), A099442 (semiprimes in A000295).

More terms from Hugo Pfoertner, Aug 13 2007
a(24) corrected by Hugo Pfoertner, Sep 07 2017
a(32)-a(44) from Tyler Busby, Jan 05 2025

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A099439 Numbers k such that A000295(k) = 2^k-k-1 is prime.

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A099440 Primes of the form A000295(k) = 2^k - k - 1.

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A099441 Numbers n such that A000295(n) = 2^n-n-1 is a semiprime.

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