

A183072


Positive integers k such that 2^k  1 is composite and each of its prime divisors has the form 4j + 3.


7



6, 10, 14, 15, 26, 30, 34, 38, 43, 51, 62, 65, 79, 85, 86, 93, 95, 122, 129, 130, 133, 158, 170, 193, 254, 255, 301, 311, 331, 349, 389, 445, 557, 577, 579, 631, 647, 1103, 1167
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Needed factorizations are in the Cunningham Project.


LINKS

Table of n, a(n) for n=1..39.
S. S. Wagstaff, Jr., The Cunningham Project.


FORMULA

A183076(n) = 2^a(n)  1.


EXAMPLE

6 is in this sequence because 2^6  1 = 3^2 * 7, and 3 and 7 have the form 4j + 3.


MATHEMATICA

c4j3Q[n_]:=Module[{c=2^n1}, CompositeQ[c]&&AllTrue[(#3)/4&/@ FactorInteger[ c] [[All, 1]], IntegerQ]]; Select[Range[650], c4j3Q] (* Requires Mathematica version 10 or later *) (* The program takes a long time to run *) (* Harvey P. Dale, Sep 23 2018 *)


CROSSREFS

Cf. A000043, A136003, A183071, A183073, A183074.
Cf. A000668, A136005, A183075, A183076, A183077, A183078.
Sequence in context: A162409 A226494 A242920 * A225704 A228301 A193416
Adjacent sequences: A183069 A183070 A183071 * A183073 A183074 A183075


KEYWORD

nonn,hard,more,changed


AUTHOR

Stuart Clary, Dec 23 2010


EXTENSIONS

a(38)a(39) from Amiram Eldar, Feb 18 2019


STATUS

approved



