login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144325 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. 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 (list; graph; refs; listen; history; text; internal format)
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;

- 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.

LINKS

Table of n, a(n) for n=1..45.

CROSSREFS

Cf. A000040, A000043, A000668, A144313, A144315

Sequence in context: A139980 A140830 A038133 * A234101 A161367 A216311

Adjacent sequences:  A144322 A144323 A144324 * A144326 A144327 A144328

KEYWORD

easy,nonn

AUTHOR

Reikku Kulon, Sep 17 2008, Sep 18 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 22:30 EST 2018. Contains 318154 sequences. (Running on oeis4.)