

A183074


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


7



43, 79, 193, 311, 331, 349, 389, 557, 577, 631, 647, 1103
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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^n1}, !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



