A050415 Primes of the form 2^k - 3.

5, 13, 29, 61, 509, 1021, 4093, 16381, 1048573, 4194301, 16777213, 536870909, 19807040628566084398385987581, 83076749736557242056487941267521533, 5316911983139663491615228241121378301

Offset

1,1

Comments

If p = 2^k - 3 is in this sequence, then p*2^(k-1) is abundant with abundance 2. - Claude Morin, Feb 01 2007

Equivalently, primes which give a prime number when 0's and 1's are interchanged in their binary representation; note that the resulting prime is always 10_2 = 2_10 (see A347476). - Bernard Schott, Nov 14 2021

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..30

Formula

a(n) = 2^A050414(n) - 3.

Mathematica

lst={}; Do[p=2^n-3; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 5*5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)
Select[Table[2^n-3, {n, 1, 400}], PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)

Prog

(Magma) [a: n in [1..200] | IsPrime(a) where a is  2^n-3]; // Vincenzo Librandi, Dec 08 2011
(PARI) for(n=3, 999, if(ispseudoprime(t=2^n-3), print1(t", "))) \\ Charles R Greathouse IV, Jul 02 2013

Crossrefs

Cf. A045768, A050414.

Subsequence of A347476.

Sequence in context: A029580 A344920 A113914 * A099970 A073857 A295112

Adjacent sequences: A050412 A050413 A050414 * A050416 A050417 A050418

Keyword

nonn

Author

Jud McCranie, Dec 22 1999

Status

approved