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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A216970 A059223 A096694 * A267490 A365405 A198245
KEYWORD
easy,nonn
AUTHOR
Reikku Kulon, Sep 17 2008
STATUS
approved

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Last modified March 28 14:13 EDT 2024. Contains 371254 sequences. (Running on oeis4.)