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A327723 a(1) = 0. For n > 1, a(n) is the smallest positive integer k not already in the sequence such that the least significant digit of k equals the most significant digit of a(n-1).

%I A327723 #23 Sep 26 2019 09:14:22
%S A327723 0,10,1,11,21,2,12,31,3,13,41,4,14,51,5,15,61,6,16,71,7,17,81,8,18,91,
%T A327723 9,19,101,111,121,131,141,151,161,171,181,191,201,22,32,23,42,24,52,
%U A327723 25,62,26,72,27,82,28,92,29,102,211,112,221,122,231,132,241,142
%N A327723 a(1) = 0. For n > 1, a(n) is the smallest positive integer k not already in the sequence such that the least significant digit of k equals the most significant digit of a(n-1).
%C A327723 Except for 0 and 10, there are no multiples of 10 (terms of A008592) in the sequence, i.e., any term of the sequence except 0 or 10 is a term of A067251.
%C A327723 Are there any numbers except multiples of 10 that do not occur in the sequence? In other words, is this a permutation of A067251 UNION [0, 10]?
%F A327723 A010879(a(n)) = A000030(a(n-1)).
%t A327723 L={0}; Do[k = IntegerDigits[ Last@ L][[1]]; While[ MemberQ[L,k], k+=10]; AppendTo[ L, k], {80}]; L (* _Giovanni Resta_, Sep 24 2019 *)
%o A327723 (PARI) isinv(vec, k) = for(t=1, #vec, if(vec[t]==k, return(1))); 0
%o A327723 isvalid(x, y) = my(d=digits(x), e=digits(y)); d[#d]==e[1]
%o A327723 terms(n) = my(v=[0, 10]); while(1, if(#v >= n, return(v)); for(k=1, oo, if(isvalid(k, v[#v]) && !isinv(v, k), v=concat(v, [k]); break)))
%o A327723 terms(100) \\ Print initial 100 terms
%o A327723 (Python)
%o A327723 n, a, msdc = 0, 0, [1,0,0,0,0,0,0,0,0,0]
%o A327723 while n <= 62:
%o A327723     print(n,a)
%o A327723     s = str(a)
%o A327723     msd = int(s[0])
%o A327723     n, a = n+1, msdc[msd]*10+msd
%o A327723     msdc[msd] = msdc[msd]+1 # _A.H.M. Smeets_, Sep 25 2019
%Y A327723 Cf. A000030, A008592, A010879, A067251.
%K A327723 nonn,base,easy
%O A327723 1,2
%A A327723 _Felix Fröhlich_, Sep 24 2019