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 A057896 Nonnegative numbers that can be written as m^k - m (with m and k nonnegative) in more than one way. 3
 0, 6, 30, 210, 240, 2184, 8190, 78120, 24299970 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The next term, if it exists, is at least 2*10^17. - David Wasserman, May 01 2002 a(10) > 10^24, if it exists. The only numbers below 10^24 that can be written as m^k+m in more than one way are 30 = 5^2+5 = 3^3+3 and 130 = 5^3+5 = 2^7+2. - Giovanni Resta, Jun 21 2018 Conjectured to be finite and complete by Bennett (2001). LINKS Michael Bennett, On some exponential equations of S. S. Pillai, Canad. J. Math. 53 (2001), 897-922. Brady Haran and Matt Parker, Why 1980 was a great year to be born... but 2184 will be better, Numberphile video (2015). Dana Mackenzie, 2184: An Absurd (and Adsurd) Tale, Integers (Electronic Journal of Combinatorial Number Theory), 18 (2018), A33. See Conjecture 3. EXAMPLE 30 is in the sequence since 30 = 2^5 - 2 = 6^2 - 6; 2184 is in the sequence since 2184 = 3^7 - 3 = 13^3 - 13. MAPLE res:= {0}: for k from 3 to 60 do   for m from 2 while m^k-m < 2^60 do      x:= m^k-m;      if assigned(R[x]) or issqr(4*x+1) then res:= res union {x}      else R[x]:= [m, k]      fi   od od: res; # Robert Israel, Oct 07 2015 CROSSREFS Cf. A000918, A057895, A308324. Sequence in context: A325950 A275953 A322170 * A336509 A147779 A054721 Adjacent sequences:  A057893 A057894 A057895 * A057897 A057898 A057899 KEYWORD more,nonn AUTHOR Henry Bottomley, Sep 26 2000 EXTENSIONS More terms from Jud McCranie, Oct 01 2000 Offset corrected by Joerg Arndt, Oct 07 2015 STATUS approved

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Last modified July 25 00:32 EDT 2021. Contains 346273 sequences. (Running on oeis4.)