A144315 Prime numbers p such that p - 1 is the fourth a-figurate number, eighth b-figurate number and possibly sixteenth c-figurate number for some a, b and c and not a d-figurate number for any nontrivial d.

149, 233, 317, 569, 653, 1493, 1913, 1997, 2417, 2837, 3089, 3593, 3677, 3761, 3929, 4013, 4349, 4517, 4937, 5021, 5189, 5273, 5441, 5693, 6197, 6449, 6869, 7457, 7541, 7793, 8297, 8969, 9137, 9221, 9473, 10061, 10313, 10733, 11069, 11321, 11489

Offset

1,1

Comments

The 37th Mersenne prime exponent (Mpe, A000043) 3021377 is a member: 3021376 is the fourth 503564-figurate number, the eighth 107908-figurate number and the sixteenth 25180-figurate number and is not a k-figurate number for any other k except 3021376 (trivially). The 44th Mersenne prime exponent 32582657 is not a member of this sequence; however, it is a (4, 8, 16, 64) k-figurate number.

It is conjectured:

- that this sequence is infinite;

- that there is a unique set {4, 8, 16, 64, ...} (A074700?) giving the possible orders in k-figurate numbers for the set S of all Mpe for which Mpe - 1 is a (4, 8) k-figurate number;

- that the ratio of Mpe in this sequence to those not approaches a nonzero value;

- that a characteristic function f(n) exists which equals 1 iff n is in S.

Links

Table of n, a(n) for n=1..41.

Crossrefs

Cf. A000040, A000043, A000668, A074700, A144313

Sequence in context: A216970 A059223 A096694 * A267490 A365405 A198245

Adjacent sequences: A144312 A144313 A144314 * A144316 A144317 A144318

Keyword

easy,nonn

Author

Reikku Kulon, Sep 17 2008

Status

approved