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
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
KEYWORD
nonn,easy
AUTHOR
Craig J. Beisel, May 20 2019
STATUS
approved