This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A113608 #16 Nov 12 2024 03:07:00 %S A113608 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 A113608 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 A113608 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 A113608 Apply the map k -> A040115(k) repeatedly to n until a single digit is reached. %C A113608 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 A113608 T. D. Noe, <a href="/A113608/b113608.txt">Table of n, a(n) for n=10..10000</a> %e A113608 a(1396) = 1 because A040115(1396) = 263, A040115(263) = 43, A040115(43) = 1. %e A113608 a(1237584965) = 1 from 6-fold application of A040115: 1237584965 -> 114234531 -> 3211122 -> 110010 -> 01011 = 1011 -> 110 -> 01 -> 1. %p A113608 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 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 %t A113608 a[n_] := NestWhile[FromDigits[Abs[Differences[IntegerDigits[#]]]] &, n, # > 9 &]; Array[a, 120, 10] (* _Amiram Eldar_, Nov 12 2024 *) %Y A113608 Cf. A040115. %K A113608 base,easy,nonn %O A113608 10,4 %A A113608 _Amarnath Murthy_, Nov 09 2005 %E A113608 Edited and extended by _R. J. Mathar_, Aug 28 2007 %E A113608 Further edited by _N. J. A. Sloane_, Aug 19 2008