

A144325


Prime numbers p such that p  1 is the third afigurate number, sixth bfigurate number and possibly twelfth cfigurate number for some a, b and c and not a dfigurate number for any nontrivial d.


3



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
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OFFSET

1,1


COMMENTS

Every member is congruent to 7 modulo 10.
The 12th Mersenne prime exponent (Mpe, A000043) 127 is a member: 126 is the third 43figurate number and the sixth 10figurate number and is not a kfigurate 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 kfigurate numbers for the set S of all Mpe for which Mpe  1 is a (3, ...) kfigurate 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 thirtyone can be characterized by this entry, A144313 and A144315; or by no more than two additional sequences related to (4, 52) and (4, 187) kfigurate numbers.


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CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



