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

%I A189710 #12 Mar 07 2018 13:24:51
%S A189710 2,3,5,7,9,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,
%T A189710 89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,
%U A189710 179,181,185,191,193,197,199,211,223,227,229,233,239,241,251,257,263
%N A189710 Numbers n such that n'' = n'-1 where n' and n'' are respectively the first and the second arithmetic derivative of n (A003415).
%C A189710 The composite numbers in the sequences are: 9, 185, 341, 377, 437, 9005, 30413, 33953, 41009, 51533, 82673, 92909,....
%H A189710 Reinhard Zumkeller, <a href="/A189710/b189710.txt">Table of n, a(n) for n = 1..10000</a>
%e A189710 9' = 6, 9''= 6'= 5, 9" = 9'- 1 -> 9 is in the sequence.
%p A189710 #using _Michael B. Porter_'s code from A003415
%p A189710 der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2])
%p A189710 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
%o A189710 (Haskell)
%o A189710 import Data.List (elemIndices)
%o A189710 a189710 n = a189710_list !! (n-1)
%o A189710 a189710_list = elemIndices 0 $
%o A189710    zipWith (-) (map a003415 a003415_list) (map pred a003415_list)
%o A189710 -- _Reinhard Zumkeller_, May 09 2011
%Y A189710 Cf. A003415, A007850, A054377, A189639.
%K A189710 nonn
%O A189710 1,1
%A A189710 _Giorgio Balzarotti_, Apr 25 2011