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

186, 258, 322, 338, 3866, 4326, 4775, 18830, 19122, 27586, 34330, 34538, 41626, 46762, 49858, 49922, 54298, 55810, 70510, 82122, 86938, 89102, 101042, 101706, 106442, 110510, 112910, 118586, 120822, 129722, 133430, 134714, 150742, 157362, 158235, 163410

Offset: 1

Author

Giorgio Balzarotti, May 01 2011

Keywords

• nonn

Comments

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

Examples

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

Links

• Donovan Johnson, Table of n, a(n) for n = 1..673

Crossrefs

Cf. A003415, A007850.

Programs

Maple

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