A050415 Primes of the form 2^k - 3.

5, 13, 29, 61, 509, 1021, 4093, 16381, 1048573, 4194301, 16777213, 536870909, 19807040628566084398385987581, 83076749736557242056487941267521533, 5316911983139663491615228241121378301, 1427247692705959881058285969449495136382746621

Offset: 1

Author

Jud McCranie, Dec 22 1999

Keywords

• nonn

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
• Christian Kassel and Christophe Reutenauer, Pairs of intertwined integer sequences, arXiv:2507.15780 [math.NT], 2025. See p. 12.

Crossrefs

Cf. A045768, A050414.

Subsequence of A347476.

Programs

Magma

[a: n in [1..200] | IsPrime(a) where a is 2^n-3]; // Vincenzo Librandi, Dec 08 2011

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 *)

PARI

for(n=3,999,if(ispseudoprime(t=2^n-3),print1(t", "))) \\ Charles R Greathouse IV, Jul 02 2013

Formula

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