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Numbers of the form 2^k - 1 for which each prime divisor has the form 4j + 3.
8

%I #9 Feb 18 2019 06:21:11

%S 1,3,7,31,63,127,1023,8191,16383,32767,131071,524287,67108863,

%T 1073741823,2147483647,17179869183,274877906943,8796093022207,

%U 2251799813685247,2305843009213693951

%N Numbers of the form 2^k - 1 for which each prime divisor has the form 4j + 3.

%C The Mersenne primes (A000668) are contained in this sequence.

%C Needed factorizations are in the Cunningham Project.

%H Amiram Eldar, <a href="/A183075/b183075.txt">Table of n, a(n) for n = 1..54</a>

%H S. S. Wagstaff, Jr., <a href="http://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>.

%F a(n) = 2^A183071(n) - 1.

%e 63 = 2^6 - 1 = 3^2 * 7, and 3 and 7 have the form 4j + 3.

%Y Cf. A000668, A136005, A183076, A183077, A183078.

%Y Cf. A000043, A136003, A183071, A183072, A183073, A183074.

%K nonn,hard

%O 1,2

%A _Stuart Clary_, Dec 23 2010