cp's OEIS Frontend

A347353 Lexicographically earliest sequence of distinct positive terms such that the rightmost digit of a(n) concatenated with the leftmost digit of a(n+1) form an integer that is the sum of the digits of a(n) and a(n+1).

%I A347353 #11 May 07 2022 10:10:08
%S A347353 1,19,1899999999,29,1799999999,119,1889999999,128,169999999,1299,
%T A347353 178999999,1389,179899999,1398,15999999,13999,16899999,14899,16989999,
%U A347353 14989,16998999,14998,1499999,149999,1589999,158999,1598999,159899,1599899,159989,1599989,159998,139999,1599999,148999
%N A347353 Lexicographically earliest sequence of distinct positive terms such that the rightmost digit of a(n) concatenated with the leftmost digit of a(n+1) form an integer that is the sum of the digits of a(n) and a(n+1).
%C A347353 In other words, the two digits squeezing a comma form the sum of the digits of the two terms squeezing the comma. This sequence is finite and has 1309 terms, the last one being 191.
%e A347353 a(1), a(2) = 1, 19 and 11 is 1 + (1+9);
%e A347353 a(2), a(3) = 19, 1899999999 and 91 is (1+9) + (1+8+9+9+9+9+9+9+9+9);
%e A347353 a(3), a(4) = 1899999999, 29 and 92 is (1+8+9+9+9+9+9+9+9+9) + (9+2);
%e A347353 a(4), a(5) = 29, 1799999999 and 91 is (2+9) + (1+7+9+9+9+9+9+9+9+9); etc.
%t A347353 a[1]=1;a[n_]:=a[n]=(t=1;While[!IntegerQ[m=Min@Union@Flatten@Table[l=FromDigits[{Last[s=IntegerDigits@a[n-1]],k}]-Total@s;Complement[FromDigits/@Flatten[Permutations/@Select[Sort/@IntegerPartitions[l,t,Range@9],First@#==k&],1],Array[a,n-1]],{k,9}]],t++];m);Array[a,35] (* _Giorgos Kalogeropoulos_, May 05 2022 *)
%Y A347353 Cf. A121805, A139284.
%K A347353 base,nonn,fini
%O A347353 1,2
%A A347353 _Eric Angelini_ and _Carole Dubois_, Aug 28 2021