cp's OEIS Frontend

A167452 Smallest sequence which lists the position of digits "2" in the sequence.

%I A167452 #6 Oct 02 2024 06:14:14
%S A167452 3,4,22,30,31,33,34,35,36,37,38,42,43,44,45,52,202,222,223,302,2220,
%T A167452 3000,3200,3300,3301,3303,3304,3305,3306,3307,3308,3309,3310,3311,
%U A167452 3313,3314,3315,3316,3317,3318,3319,3330,3331,3333,3334,3335,3336,3337,3338
%N A167452 Smallest sequence which lists the position of digits "2" in the sequence.
%C A167452 The lexicographically earliest sequence such that a(1),a(2),a(3),... is the (increasing) list of the positions of digits "1" in the string obtained by concatenating all these terms, written in base 10.
%e A167452 We cannot have a(1)=1 (since then there's no 2 in the first place), nor a(1)=2 (since then the first occurrence of a "2" would be at position 1).
%e A167452 But a(1)=3 is possible, "predicting" that the first occurrence of a digit "2" will be in the 3rd digit.
%e A167452 Then a(2)=4 is the smallest possible choice for a(2).
%e A167452 The next two digits (= the 3rd and 4th digit of the sequence) must be a "2", in view of a(1) and a(2). Thus a(3)=22 is the smallest possible choice.
%e A167452 This means that the next digit "2" will occur as the 22nd digit of the sequence, so the following terms are the least possible numbers without digit "2": 30,31,33,...,38. These make up digits 5 to 20 of the sequence.
%e A167452 The following number must have a "2" as second digit, the smallest possibility is 42.
%o A167452 (PARI) concat([ [3,4,22], vector((22-4)/2-1,i,i+30-(i<=2)), vector(4,i,42+i-1), [52,202,222,223,302,2220,3000,3200], select(x -> x%10-2 & x\10%10-2 & x\100%10-2, vector((202-52)\4+13,i,3300+i-1)) ])
%Y A167452 Cf. A098645, A167519, A167520.
%K A167452 base,nonn,nice
%O A167452 1,1
%A A167452 _M. F. Hasler_, Nov 19 2009