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

1,1

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.

Links

Table of n, a(n) for n=1..42.

Formula

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

Example

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

Mathematica

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

Crossrefs

Subsequence of A054723.

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

Sequence in context: A181622 A355599 A086149 * A066502 A125870 A076439

Adjacent sequences: A344512 A344513 A344514 * A344516 A344517 A344518

Keyword

nonn,more

Author

Amiram Eldar, May 21 2021

Status

approved