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%I #19 Jan 10 2018 11:31:19
%S 0,0,0,0,0,52,0,11,0,0,51,50,0,49,10,0,0,48,0,9,50,0,49,0,0,47,48,0,0,
%T 8,0,49,46,0,47,48,0,45,0,0,7,46,7,47,6,0,45,44,6,0,46,0,5,5,0,45,44,
%U 0,43,4,5,4,0,0,4,44,4,43,3,0,0,42,0,3,3,4,43,0
%N Define a sequence b_s by b_s(1)=s, b_s(k+1)=b_s(k)+(sum of digits of b_s(k)); a(n) is the number of steps needed for b_n to reach a term in one of b_0, b_1, b_3 or b_9, or a(n) = -1 if b_n never joins one of these four sequences.
%C We conjecture that a(n) is never -1.
%H Lars Blomberg, <a href="/A230299/b230299.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%p read transforms; # to get digsum
%p M:=2000;
%p # f(s) returns the sequence k->k+digsum(k) starting at s
%p f:=proc(s) global M; option remember; local n,k,s1;
%p s1:=[s]; k:=s;
%p for n from 1 to M do k:=k+digsum(k);
%p s1:=[op(s1),k]; od: end;
%p # g(s) returns (x,p), where x = first number in common between
%p # f(s) and one of f(1), f(3), f(9) and p is the position where it occurred.
%p # If f(s) and all of f(1), f(3), f(9) are disjoint for M terms, returns (-1,-1)
%p S1:=convert(f(1),set):
%p S3:=convert(f(3),set):
%p S9:=convert(f(9),set):
%p g:=proc(s) global f,S1,S3,S9; local t1,p,T0,T1,T2;
%p T0:=f(s):
%p T1:=convert(T0,set);
%p if ((s mod 9) = 3) or ((s mod 9) = 6) then T2:= T1 intersect S3; t1:=min(T2); if (t1 = infinity) then RETURN(-1,-1); else member(t1,T0,'p'); RETURN(t1,p-1); fi;
%p elif ((s mod 9) = 0) then T2:= T1 intersect S9; t1:=min(T2); if (t1 = infinity) then RETURN(-1,-1); else member(t1,T0,'p'); RETURN(t1,p-1); fi;
%p else T2:= T1 intersect S1; t1:=min(T2); if (t1 = infinity) then RETURN(-1,-1); else member(t1,T0,'p'); RETURN(t1,p-1); fi;
%p fi;
%p end;
%p [seq(g(n)[2],n=1..45)];
%Y Cf. A230107, A062028, A004207, A016052, A007618, A006507, A016096.
%K nonn,base,look
%O 0,6
%A _N. J. A. Sloane_ and _Reinhard Zumkeller_, Oct 21 2013
%E Terms a(46) and beyond from _Lars Blomberg_, Jan 10 2018
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