A189639 Numbers n such that n'' = n'+1 where n' and n'' are respectively the first and the second arithmetic derivative of n (A003415).

161, 209, 221, 1935, 4265, 15941, 22217, 24041, 25637, 30377, 38117, 39077, 48617, 49097, 55877, 68441, 73817, 76457, 80357, 88457, 95237, 98117, 99941, 105641, 110057, 115397, 122537, 130217, 131141, 136517, 143237, 147941, 148697, 152357, 154457, 159077

Offset: 1

Author

Giorgio Balzarotti, Apr 24 2011

Keywords

• nonn
• look

Comments

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

Examples

			161' = 30, 161'' = 30' = 31 ==> 161'' = 161'+1 so 161 is a term.
		

Links

• Reinhard Zumkeller and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 100 terms from Reinhard Zumkeller)

Crossrefs

Cf. A003415, A007850, A054377, A132632, A189639.

Programs

Haskell

import Data.List (elemIndices)
a189710 n = a189710_list !! (n-1)
a189710_list = elemIndices 0 $
   zipWith (-) (map a003415 a003415_list) (map pred a003415_list)
-- Reinhard Zumkeller, May 09 2011

PARI

/* using Michael B. Porter's code from A003415: */
A003415(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))} /* arithmetic derivative */
for(n=1,10^6,d1=A003415(n);d2=A003415(d1);if(d2==d1+1,print1(n,", "))); /* show terms */
/* Joerg Arndt, Apr 25 2011 */