A153443 Aurifeuillian primes of the form 2^k+1

3, 5, 11, 13, 17, 43, 241, 257, 331, 683, 2731, 5419, 43691, 61681, 65537, 174763, 2796203, 15790321, 18837001, 22366891, 715827883, 4278255361, 4562284561, 77158673929, 1133836730401, 2932031007403, 4363953127297

Offset

1,1

Comments

Take an irreducible real factor of x^k+1 and substitute x=2. If the result is a prime then it belongs in this sequence. For example for k=5 the polynomial x^5+1=(x+1)(x^4-x^3+x^2-x+1) and substituting x->2 in (x^4-x^3+x^2-x+1) we get the prime number 11. So 11 is a term. [Clarified by N. J. A. Sloane, Jul 03 2020]

Links

Table of n, a(n) for n=1..27.

Crossrefs

A061442.

Sequence in context: A227011 A243627 A178604 * A211876 A374050 A066587

Adjacent sequences: A153440 A153441 A153442 * A153444 A153445 A153446

Keyword

nonn

Author

Artur Jasinski, Dec 26 2008

Status

approved