

A183075


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


8



1, 3, 7, 31, 63, 127, 1023, 8191, 16383, 32767, 131071, 524287, 67108863, 1073741823, 2147483647, 17179869183, 274877906943, 8796093022207, 2251799813685247, 2305843009213693951
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The Mersenne primes (A000668) are contained in this sequence.
Needed factorizations are in the Cunningham Project.


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..54
S. S. Wagstaff, Jr., The Cunningham Project.


FORMULA

a(n) = 2^A183071(n)  1.


EXAMPLE

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


CROSSREFS

Cf. A000668, A136005, A183076, A183077, A183078.
Cf. A000043, A136003, A183071, A183072, A183073, A183074.
Sequence in context: A145479 A077315 A080168 * A292890 A042131 A109140
Adjacent sequences: A183072 A183073 A183074 * A183076 A183077 A183078


KEYWORD

nonn,hard


AUTHOR

Stuart Clary, Dec 23 2010


STATUS

approved



