|
|
A188145
|
|
Solutions of the equation n" - n' - n = 0, where n' and n" are the first and second arithmetic derivatives (see A003415).
|
|
1
|
|
|
0, 20, 135, 164, 1107, 15625, 43692, 128125, 188228, 294921, 1270539, 4117715, 33765263, 34134375, 147053125, 8995560189, 19348535652, 38753462951
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Solutions of the similar equation n”-n’+n=0 are 30, 858, 1722, etc., apparently Giuga numbers whose derivative is a prime number. In fact the equation can be rewritten as n'=n+n" and if n"=1 it is the conjecture in A007850.
|
|
LINKS
|
|
|
EXAMPLE
|
n=20, n’=24, n”=44 -> 44-24-20=0; n=135, n’=162, n”=297 -> 297-162-135=0
|
|
MAPLE
|
readlib(ifactors):
Der:= proc(n)
local a, b, i, p, pfs;
for i from 0 to n do
if i<=1 then a:=0;
else pfs:=ifactors(i)[2]; a:=i*add(op(2, p)/op(1, p), p=pfs) ;
fi;
if a<=1 then b:=0;
else pfs:=ifactors(a)[2]; b:=a*add(op(2, p)/op(1, p), p=pfs) ;
fi;
if b-a=i then lprint(i, a, b); fi;
od
end:
Der(10000000);
|
|
PROG
|
(Haskell)
import Data.List (zipWith3, elemIndices)
a188145 n = a188145_list !! (n-1)
a188145_list = elemIndices 0 $ zipWith3 (\x y z -> x - y - z)
(map a003415 a003415_list) a003415_list [0..]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|