%I #12 Aug 09 2015 00:29:33
%S 1,0,1,2,3,4,5,6,7,8,2,1,0,1,2,3,4,5,6,7,3,2,1,0,1,2,3,4,5,6,4,3,2,1,
%T 0,1,2,3,4,5,5,4,3,2,1,0,1,2,3,4,6,5,4,3,2,1,0,1,2,3,7,6,5,4,3,2,1,0,
%U 1,2,8,7,6,5,4,3,2,1,0,1,9,8,7,6,5,4,3,2,1,0,1,0,1,2,3,4,5,6,7,8,1
%N Apply the map k > A040115(k) repeatedly to n until a single digit is reached.
%C Leading zeros at any intermediate result are discarded. The first terms, from n=10 to n=99, are identical to A040115.  _R. J. Mathar_, Aug 28 2007
%H T. D. Noe, <a href="/A113608/b113608.txt">Table of n, a(n) for n=10..10000</a>
%e a(1396)=1 because A040115(1396)=263, A040115(263)=43, A040115(43)=1.
%e a(1237584965)=1 from 6fold application of A040115: 1237584965>114234531 > 3211122 > 110010 > 01011=1011 > 110 > 01 > 1.
%p A040115 := proc(n) local digs,digsdiff,i; digsdiff := [] ; digs := convert(n,base,10) ; for i from 2 to nops(digs) do digsdiff := [op(digsdiff),abs(op(i,digs)op(i1,digs))] ; od; add( op(i,digsdiff)*10^(i1),i=1..nops(digsdiff)) ; end:
%p A113608 := proc(n) local a; a := A040115(n) ; while a>9 do a := A040115(a) ; od; RETURN(a) ; end: seq(A113608(n),n=10..110) ; # _R. J. Mathar_, Aug 28 2007
%Y Cf. A040115.
%K base,easy,nonn
%O 10,4
%A _Amarnath Murthy_, Nov 09 2005
%E Edited and extended by _R. J. Mathar_, Aug 28 2007
%E Further edited by _N. J. A. Sloane_, Aug 19 2008
