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 A113608 Apply the map k -> A040115(k) repeatedly to n until a single digit is reached. 1

%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 6-fold 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(i-1,digs))] ; od; add( op(i,digsdiff)*10^(i-1),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

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Last modified April 13 20:16 EDT 2024. Contains 371645 sequences. (Running on oeis4.)