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Form the sum of the digits of a(n); a(n+1) is the smallest unused integer having a copy of every digit of this sum.
1

%I #10 Mar 08 2015 20:42:35

%S 0,10,1,11,2,12,3,13,4,14,5,15,6,16,7,17,8,18,9,19,100,21,23,25,27,29,

%T 101,20,22,24,26,28,102,30,31,34,37,103,40,41,35,38,110,32,45,39,112,

%U 42,36,49,113,50,51,46,104,52,47,111,33,56,114,60,61,57,120,43,67,123,62

%N Form the sum of the digits of a(n); a(n+1) is the smallest unused integer having a copy of every digit of this sum.

%C The "seed" is 0 in this case.

%C This is a permutation of the nonnegative integers. - Nadia Heninger, Aug 10 2005

%H R. J. Mathar, Feb 21 2008, <a href="/A107408/b107408.txt">Table of n, a(n) for n = 0..93</a>

%H N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

%e Sum of the digits of 29 is 11; the smallest available integer which has a copy of every digit of 11 is 101 (not 31).

%p A007953 := proc(n) add(i,i=convert(n,base,10)) ; end: multDigs := proc(n) local a,dgs,i; if n = 0 then a := [1,seq(0,i=1..9)] ; else a := [seq(0,i=0..9)] ; dgs := convert(n,base,10) ; for i in dgs do a := subsop(i+1=op(i+1,a)+1,a) ; od: fi ; RETURN(a) ; end: A107408 := proc(nmax) local a,ds,dsk,k,works,d ; a := [0] ; while nops(a) < nmax do ds := multDigs(A007953(op(-1,a))) ; for k from 1 do if not k in a then dsk := multDigs(k) ; works := true; for d from 1 to 10 do if op(d,dsk) < op(d,ds) then works := false ; break ; fi ; od: if works then a := [op(a),k] ; break ; fi ; fi ; od: od: RETURN(a) ; end: A107408(120) ; # _R. J. Mathar_, Feb 21 2008

%K base,easy,nonn

%O 0,2

%A _Eric Angelini_, Jun 09 2005

%E Corrected and extended by _R. J. Mathar_, Feb 21 2008