|
|
A057896
|
|
Nonnegative numbers that can be written as m^k - m (with m and k nonnegative) in more than one way.
|
|
3
|
|
|
|
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
|
|
|
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:
|
|
CROSSREFS
|
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|