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A189941 Numbers n such that n''' = n''+ 1 where n'' and n''' are respectively the second and the third arithmetic derivative of n. 2

%I #9 Mar 31 2012 10:28:21

%S 186,258,322,338,3866,4326,4775,18830,19122,27586,34330,34538,41626,

%T 46762,49858,49922,54298,55810,70510,82122,86938,89102,101042,101706,

%U 106442,110510,112910,118586,120822,129722,133430,134714,150742,157362,158235,163410

%N Numbers n such that n''' = n''+ 1 where n'' and n''' are respectively the second and the third arithmetic derivative of n.

%C The second arithmetic derivative of a(n) is a Giuga's number A007850 (solution of n'=n+1).

%H Donovan Johnson, <a href="/A189941/b189941.txt">Table of n, a(n) for n = 1..673</a>

%e 186'= 161; 186"=161' = 30; 186"'=30'= 31-> 186'''= 186" +1 -> a(1)=186.

%p Using Porter's code from A003415 der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2])

%p for i from 1 to n do a:=der(der(der(i)))-der(der(i))-1: if a=0 then j:=j+1; A[j]:=i: end if od

%Y Cf. A003415, A007850.

%K nonn

%O 1,1

%A _Giorgio Balzarotti_, May 01 2011

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