

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

T. D. Noe, Table of n, a(n) for n=10..10000


EXAMPLE

a(1396)=1 because A040115(1396)=263, A040115(263)=43, A040115(43)=1.
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

Cf. A040115.
Sequence in context: A040114 A064834 A040163 * A040115 A080465 A347689
Adjacent sequences: A113605 A113606 A113607 * A113609 A113610 A113611


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



