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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

Table of n, a(n) for n=1..9.

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 * A147779 A054721 A074111

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 October 17 16:34 EDT 2019. Contains 328118 sequences. (Running on oeis4.)