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Search: id:A144325
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| A144325 |
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Prime numbers p such that p - 1 is the third a-figurate number, sixth b-figurate number and possibly twelfth c-figurate number for some a, b and c and not a d-figurate number for any nontrivial d. |
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4
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| 97, 127, 157, 307, 337, 367, 487, 547, 607, 757, 787, 907, 967, 997, 1087, 1117, 1237, 1447, 1567, 1627, 1657, 1747, 1777, 1867, 1987, 2287, 2437, 2617, 2647, 2677, 2767, 2797, 2857, 2887, 3067, 3217, 3307, 3457, 3517, 3547, 3607, 3637, 3727, 3847, 3907
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Every member is congruent to 7 modulo 10.
The 12th Mersenne prime exponent (Mpe, A000043) 127 is a member: 126 is the third 43-figurate number and the sixth 10-figurate number and is not a k-figurate number for any other k except 126 (trivially). Several other Mersenne prime exponents are members of this sequence; the next is 607.
It is conjectured:
- that this sequence is infinite;
- that there is a unique set {3, 6, 8, 12, 24, 36, ...} giving the possible orders in k-figurate numbers for the set S of all Mpe for which Mpe - 1 is a (3, ...) k-figurate number;
- that the ratio of Mpe in S to those not approaches one;
- that a characteristic function f(n) exists which equals 1 iff n is in S;
- that all Mersenne primes greater than thirty-one can be characterized by this entry, A144313 and A144315; or by no more than two additional sequences related to (4, 52) and (4, 187) k-figurate numbers.
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CROSSREFS
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Cf. A000040, A000043, A000668, A144313, A144315
Sequence in context: A139980 A140830 A038133 this_sequence A161367 A073076 A157213
Adjacent sequences: A144322 A144323 A144324 this_sequence A144326 A144327 A144328
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KEYWORD
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easy,nonn
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AUTHOR
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Reikku Kulon (reikku(AT)gmail.com), Sep 17 2008, Sep 18 2008
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