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 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;
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Reikku Kulon, Sep 17 2008, Sep 18 2008
STATUS
approved