A099441 -id:A099441 - 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 *)

A099442 Semiprimes of the form 2^k-k-1.

Original entry on oeis.org

4, 26, 57, 247, 502, 4083, 1073741793, 4294967263, 8589934558, 70368744177617, 4503599627370443, 4611686018427387841, 18889465931478580854709, 75557863725914323419059, 77371252455336267181195177, 316912650057057350374175801245

Offset: 1

Hugo Pfoertner, Oct 18 2004

nonn

Semiprimes in A000295.

			a(4) = 247 because 247 = 13*19 = 2^8-8-1 = 2^A099441(4)-A099441(4)-1.

Hugo Pfoertner, Table of n, a(n) for n = 1..31 (first 19 terms from Vincenzo Librandi)

Cf. A099439, A099440, A099441.

Select[Table[2^n - n - 1, {n, 300}], PrimeOmega[#] == 2&] (* Vincenzo Librandi, Sep 21 2012 *)

from sympy.ntheory.factor_ import primeomega
def ok(n): return primeomega(2**n-n-1) == 2
print([2**m-m-1 for m in range(2, 100) if ok(m)]) # Michael S. Branicky, Apr 26 2021

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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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A099442 Semiprimes of the form 2^k-k-1.

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