A344515 Primes p such that 2^p-1 has exactly 3 distinct prime factors.

29, 43, 47, 53, 71, 73, 79, 179, 193, 211, 257, 277, 283, 311, 331, 349, 353, 389, 409, 443, 467, 499, 563, 577, 599, 613, 631, 643, 647, 683, 709, 751, 769, 829, 919, 941, 1039, 1103, 1117, 1123, 1171, 1193

Offset: 1

Author

Amiram Eldar, May 21 2021

Keywords

• nonn
• more

Comments

The corresponding Mersenne numbers are in A135977.

a(43) >= 1237.

The following primes are also terms of this sequence: 1301, 1303, 1327, 1459, 1531, 1559, 1907, 2311, 2383, 2887, 3041, 3547, 3833, 4127, 4507, 4871, 6883, 7673, 8233.

Examples

			29 is a term since 2^29-1 = 536870911 = 233 * 1103 * 2089 has exactly 3 distinct prime factors.
		

Crossrefs

Subsequence of A054723.

Cf. A000225, A065341, A135975, A135976, A135977, A135978.

Programs

Mathematica

Select[Range[200], PrimeQ[#] && PrimeNu[2^# - 1] == 3 &]

Formula

2^a(n) - 1 = A135977(n).