A341037 - OEIS

%I #24 May 11 2022 17:32:18

%S 1,3,5,30,12,4,10,6,2,26,23,75,72,40,16,33,44,54,93,406,592,4407,5591,

%T 44408,55590,4398,5600,44399,55599,94398,393325,106674,8303,1695,800,

%U 198,96,51,47,452,546,42,56,8,20,15,9,89,410,80,18,24,25,45,53,446

%N The successive remainders of the division by (a(n) + a(n+1)) of concat(a(n),a(n+1)) rebuild the sequence itself.

%C Lexicographically earliest sequence of distinct terms > 0 with this property.

%C The sequence is conjectured to be a permutation of the integers > 0.

%e    1 and 3  ->   13/4  with remainder  1

%e    3 and 5  ->   35/8  with remainder  3

%e    5 and 30 ->  530/35 with remainder  5

%e   30 and 12 -> 3012/42 with remainder 30

%e   12 and 4  ->  124/16 with remainder 12

%e    4 and 10 ->  410/14 with remainder  4

%e   10 and 6  ->  106/16 with remainder 10

%e    6 and 2  ->   62/8  with remainder  6; etc.

%e The first and last column are identical.

%t a[1]=1;a[n_]:=a[n]=Block[{k=1},While[MemberQ[Array[a,n-1],k]||Mod[FromDigits@Flatten[IntegerDigits/@{a[n-1],k}],a[n-1]+k]!=a[n-1],k++];k];Array[a,27] (* _Giorgos Kalogeropoulos_, May 11 2022 *)

%o (PARI) lista(nn) = {my(k, v=vector(nn)); v[1]=1; for(i=1, nn-1, k=1; until(eval(Str(v[i], k))%(v[i]+k)==v[i]&&!vecsearch(vecsort(v), k), k++); v[i+1]=k); v; } \\ _Jinyuan Wang_, Feb 10 2021

%Y Cf. A095245.

%K nonn,base

%O 1,2

%A _Eric Angelini_, Feb 03 2021

%E More terms from _Jinyuan Wang_, Feb 10 2021