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%I #14 Jan 25 2024 07:54:07
%S 10,100,101,90,91,80,81,70,71,60,61,50,51,40,41,30,31,20,21,102,82,62,
%T 42,200,201,103,72,52,32,104,63,300,301,210,105,53,211,106,43,107,302,
%U 108,220,221,109,110,112,92,73,400,401,310,113,83,54,114,74,311
%N Last digit of a(n) + first digit of a(n+1) occurs as a substring in a(n); lexicographic first sequence with this property and no duplicates.
%C A permutation of the numbers of the form 10k+z, 0 <= z <= 9, k having a digit > z or a digit 1 followed by a digit < z.
%C Sequence suggested by _Eric Angelini_, first 500 terms independently computed by _Jack Brennen_, cf. link to SeqFan list.
%H M. F. Hasler, <a href="/A268449/b268449.txt">Table of n, a(n) for n = 1..10000</a>
%H E. Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2016-February/016064.html">A sum visible in the 1st integer</a>, and replies to this post, SeqFan list, Feb. 4, 2016.
%o (PARI) EA(n,a=List(10),u=[0])={ my(isok(n)=vecmax(n=digits(n))>n[#n] || sum(i=1,#n-2, n[i]==1 && n[i+1]<n[#n])); for(n=1,n-1,u=setunion(u,[a[n]]); until( isok(u[1]+1) || !u[1]++ , while(#u>1&&u[2]==u[1]+1, u=u[^1])); ok=setintersect(apply(t->t-a[n]%10,Set(concat(ok=digits(a[n]), vector(#ok-1, i, ok[i+1]+ok[i]*10)))), [1..9]); for(k=u[1]+1,9e9, setsearch(u,k) && next; isok(k) || next; setsearch(ok,digits(k)[1]) && listput(a,k) && break; k=digits(k);k=(k[1]+1)*10^(#k-1)-1)); Vec(a)}
%Y Cf. A267759 (admissible numbers; range of this sequence).
%Y Cf. A267760, A267761, A267762, A267771, A267772.
%K nonn,base,look
%O 1,1
%A _M. F. Hasler_, Feb 04 2016
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