A189710 Numbers n such that n'' = n'-1 where n' and n'' are respectively the first and the second arithmetic derivative of n (A003415).

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 185, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263

Offset: 1

Author

Giorgio Balzarotti, Apr 25 2011

Keywords

• nonn

Comments

The composite numbers in the sequences are: 9, 185, 341, 377, 437, 9005, 30413, 33953, 41009, 51533, 82673, 92909,....

Examples

			9' = 6, 9''= 6'= 5, 9" = 9'- 1 -> 9 is in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A007850, A054377, 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

Maple

#using Michael B. 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(i))-der(i)+1; if a=0 then j:=j+1; B[j]:=i; end if od