

A113608


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


1



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, 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, 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
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OFFSET

10,4


COMMENTS

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


LINKS



EXAMPLE

a(1237584965)=1 from 6fold application of A040115: 1237584965>114234531 > 3211122 > 110010 > 01011=1011 > 110 > 01 > 1.


MAPLE

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:
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


CROSSREFS



KEYWORD

base,easy,nonn


AUTHOR

_Amarnath Murthy_, Nov 09 2005


EXTENSIONS

Edited and extended by _R. J. Mathar_, Aug 28 2007
Further edited by _N. J. A. Sloane_, Aug 19 2008


STATUS

approved



