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A329447 Look left and tell the least frequent: after a(0) = 0, a(n) = 10c + d, where c > 0 is the number of times the least frequent digit d has appeared so far; smallest d in case of tie. 5

%I #23 Nov 16 2019 15:59:47

%S 0,10,11,20,12,22,30,13,23,33,40,14,24,34,44,50,15,25,35,45,55,60,16,

%T 26,36,46,56,66,70,17,27,37,47,57,67,77,80,18,28,38,48,58,68,78,88,90,

%U 19,29,39,49,59,69,79,89,99,100,112,113,114,115,116,117,118,119,120,123,124,125,126,127,128,129

%N Look left and tell the least frequent: after a(0) = 0, a(n) = 10c + d, where c > 0 is the number of times the least frequent digit d has appeared so far; smallest d in case of tie.

%C The terms "10c + d" are to be read "c digits d (have appeared so far)", as in the "look and see" sequences A045918 and similar.

%C An analog sequence may be computed for any other initial term a(0). Sequence A329448 lists the starting values that will appear a second time later in the respective sequence.

%H M. F. Hasler, <a href="/A329447/b329447.txt">Table of n, a(n) for n = 0..10000</a> (independently computed by _Jean-Marc Falcoz_).

%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2019/11/look-left-and-say.html">Look left and say</a>, Nov 14 2019.

%p a[0]:= 0;

%p S[0]:= 1:

%p for i from 1 to 9 do S[i]:= 0 od:

%p for n from 1 to 100 do

%p a[n]:= min(select(`>=`,[seq(10*S[i]+i, i=0..9)],10));

%p L:= convert(a[n],base,10);

%p for d from 0 to 9 do S[d]:= S[d] + numboccur(d,L) od;

%p od:

%p seq(a[n],n=0..100); # _Robert Israel_, Nov 14 2019

%o (PARI) A329447_vec(N)={my(c=Vec(1,10),t); vector(N,i, for(j=1, #i=vecsort(c,,1), if(c[i[j]], i=i[j];break)); for(j=1, #i=digits(t=c[i]*10+i-1), c[i[j]+1]++);t)} \\ Returns the vector a(1..N)

%Y Cf. A045918 (describe n), A005150 (describe the preceding term), A139282 (count vowels so far), A139097 (count letters so far).

%K nonn,base

%O 0,2

%A _Eric Angelini_ and _M. F. Hasler_, Nov 14 2019

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