OFFSET
1,1
COMMENTS
Appears to be necessarily a subset of A007528.
The 46th Mersenne prime exponent (Mpe, A000043) 43112609 is a member: 43112608 is the fourth 7185436-figurate number and the seventh 2052983-figurate number and is not a k-figurate number for any other k except 43112608 (trivially). Several other Mersenne prime exponents are members of this sequence.
It is conjectured:
- that this sequence is infinite;
- that there is a unique set {4, 7, 10, 16, ...} (A138694?) giving the possible orders in k-figurate numbers for the set S of all Mpe for which Mpe - 1 is a (4, 7) or (4, 10) 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.
Contribution from Reikku Kulon, Sep 18 2008: (Start)
Subset of the integers n such that n is congruent to 29 modulo 42. The case where p - 1 is a tenth c-figurate number occurs when p is also congruent to 281 modulo 630.
The first three primes where c is defined are 281, 911 and 2801, with c = 8, 22, 64; c is congruent to 8 modulo 14. All such primes are necessarily congruent to 1 modulo 10.
CROSSREFS
Contribution from Reikku Kulon, Sep 18 2008: (Start)
KEYWORD
easy,nonn
AUTHOR
Reikku Kulon, Sep 17 2008
STATUS
approved