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A308324 Numbers which can be written in the form m^k - m with m an odd prime and k a positive integer. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A103678 A020889 A084682 * A044970 A316291 A090502

Adjacent sequences:  A308321 A308322 A308323 * A308325 A308326 A308327

KEYWORD

nonn,easy

AUTHOR

Craig J. Beisel, May 20 2019

STATUS

approved

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Last modified February 25 11:26 EST 2020. Contains 332233 sequences. (Running on oeis4.)