A183074 Prime numbers p such that 2^p - 1 is composite and each of its prime divisors has the form 4j + 3.

43, 79, 193, 311, 331, 349, 389, 557, 577, 631, 647, 1103

Offset

1,1

Comments

Needed factorizations are in the Cunningham Project.

Links

Table of n, a(n) for n=1..12.

S. S. Wagstaff, Jr., The Cunningham Project.

Formula

A183078(n) = 2^a(n) - 1.

Example

43 is in this sequence because 2^43 - 1 = 431 * 9719 * 2099863, and each of those primes has the form 4j + 3.

Mathematica

cQ[n_]:=Module[{x=2^n-1}, !PrimeQ[x]&&Union[Mod[Transpose[ FactorInteger[ x]][[1]], 4]]=={3}]; Select[Prime[Range[120]], cQ] (* Harvey P. Dale, Jun 17 2014 *)

Crossrefs

Cf. A000043, A136003, A183071, A183072, A183073.

Cf. A000668, A136005, A183075, A183076, A183077, A183078.

Sequence in context: A121957 A118075 A236839 * A289730 A045238 A139982

Adjacent sequences: A183071 A183072 A183073 * A183075 A183076 A183077

Keyword

nonn,hard

Author

Stuart Clary, Dec 23 2010

Extensions

a(12) from Amiram Eldar, Feb 18 2019

Status

approved