A308324 Numbers which can be written in the form m^k - m with m an odd prime and k a positive integer.

0, 6, 20, 24, 42, 78, 110, 120, 156, 240, 272, 336, 342, 506, 620, 726, 812, 930, 1320, 1332, 1640, 1806, 2162, 2184, 2394, 2756, 3120, 3422, 3660, 4422, 4896, 4970, 5256, 6162, 6558, 6806, 6840, 7832, 9312

Offset

1,2

Comments

Besides the trivial example a(1)=0, the only known term which has two representations is a(24) = 2184 = 3^7 - 3 = 13^3 - 13. It is conjectured by Bennett to be the only term with this property.

Links

Table of n, a(n) for n=1..39.

Michael Bennett, On some exponential equations of S. S. Pillai, Canad. J. Math. 53 (2001), 897-922.

Dana Mackenzie, 2184: An Absurd (and Adsurd) Tale, Integers (Electronic Journal of Combinatorial Number Theory), 18 (2018), A33.

Example

a(3) = 5^2 - 5 = 20.

Prog

(PARI) x=List([]); lim=10000; forprime(m=3, lim, for(k=1, 100, y=(m^k-m); if(y>lim, break, i=setsearch(x, y, 1); if(i>0, listinsert(x, y, i))))); for(i=1, #x, print(x[i]));

Crossrefs

Cf. A057895, A246068.

Sequence in context: A334817 A084682 A341298 * A044970 A345910 A316291

Adjacent sequences: A308321 A308322 A308323 * A308325 A308326 A308327

Keyword

nonn,easy

Author

Craig J. Beisel, May 20 2019

Status

approved