cp's OEIS Frontend

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

%I A308324 #15 May 23 2019 14:46:55
%S A308324 0,6,20,24,42,78,110,120,156,240,272,336,342,506,620,726,812,930,1320,
%T A308324 1332,1640,1806,2162,2184,2394,2756,3120,3422,3660,4422,4896,4970,
%U A308324 5256,6162,6558,6806,6840,7832,9312
%N A308324 Numbers which can be written in the form m^k - m with m an odd prime and k a positive integer.
%C A308324 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.
%H A308324 Michael Bennett, <a href="https://doi.org/10.4153/CJM-2001-036-6">On some exponential equations of S. S. Pillai</a>, Canad. J. Math. 53 (2001), 897-922.
%H A308324 Dana Mackenzie, <a href="http://math.colgate.edu/~integers/s33/s33.Abstract.html">2184: An Absurd (and Adsurd) Tale</a>, Integers (Electronic Journal of Combinatorial Number Theory), 18 (2018), A33.
%e A308324 a(3) = 5^2 - 5 = 20.
%o A308324 (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]));
%Y A308324 Cf. A057895, A246068.
%K A308324 nonn,easy
%O A308324 1,2
%A A308324 _Craig J. Beisel_, May 20 2019