A183075 Numbers of the form 2^k - 1 for which each prime divisor has the form 4j + 3.

1, 3, 7, 31, 63, 127, 1023, 8191, 16383, 32767, 131071, 524287, 67108863, 1073741823, 2147483647, 17179869183, 274877906943, 8796093022207, 2251799813685247, 2305843009213693951

Offset: 1

Author

Stuart Clary, Dec 23 2010

Keywords

• nonn
• hard

Comments

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

Needed factorizations are in the Cunningham Project.

Examples

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

Links

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

Crossrefs

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

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

Formula

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