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.

0, 10, 11, 20, 12, 22, 30, 13, 23, 33, 40, 14, 24, 34, 44, 50, 15, 25, 35, 45, 55, 60, 16, 26, 36, 46, 56, 66, 70, 17, 27, 37, 47, 57, 67, 77, 80, 18, 28, 38, 48, 58, 68, 78, 88, 90, 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

Offset

0,2

Comments

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.

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.

Links

M. F. Hasler, Table of n, a(n) for n = 0..10000 (independently computed by Jean-Marc Falcoz).

Eric Angelini, Look left and say, Nov 14 2019.

Maple

a[0]:= 0;
S[0]:= 1:
for i from 1 to 9 do S[i]:= 0 od:
for n from 1 to 100 do
  a[n]:= min(select(`>=`, [seq(10*S[i]+i, i=0..9)], 10));
  L:= convert(a[n], base, 10);
  for d from 0 to 9 do S[d]:= S[d] + numboccur(d, L) od;
od:
seq(a[n], n=0..100); # Robert Israel, Nov 14 2019

Prog

(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)

Crossrefs

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

Sequence in context: A216996 A165265 A329818 * A352339 A197652 A261909

Adjacent sequences: A329444 A329445 A329446 * A329448 A329449 A329450

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Nov 14 2019

Status

approved