A363872 - OEIS

%I #19 Aug 02 2023 11:52:52

%S 1,9,3,10,4,11,5,2,6,13,87,23,89,24,90,25,91,26,92,27,93,28,94,29,95,

%T 30,96,31,97,32,98,33,99,34,100,35,101,36,102,37,103,38,104,39,105,40,

%U 106,41,7,42,8,43,109,44,110,45,111,46,12,47,113,48,14,49,15

%N Lexicographically earliest sequence of distinct terms > 0 such that n is a substring of a(n) + a(n+1).

%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2023/07/echecs-et-maths.html">Échecs et Maths</a>, Personal blog, bottom of page.

%e n = 1 is a substring of the sum  1 +  9 = 10

%e n = 2 is a substring of the sum  9 +  3 = 12

%e n = 3 is a substring of the sum  3 + 10 = 13

%e n = 4 is a substring of the sum 10 +  4 = 14

%e n = 5 is a substring of the sum  4 + 11 = 15

%e n = 6 is a substring of the sum 11 +  5 = 16

%e ...

%e n = 10 is a substring of the sum 13 + 87 = 100, etc.

%p R:= 1: x:= 1: S:= {1}:

%p for n from 1 to 100 do

%p   ns:= convert(n,string);

%p   for y from 1 do

%p     if member(y,S) then next fi;

%p     if SearchText(ns,convert(x+y,string)) <> 0 then

%p       R:= R,y; x:= y; S:= S union {y}; break

%p     fi

%p   od

%p od:

%p R;  # _Robert Israel_, Jul 04 2023

%t a[1] = 1; a[n_] := a[n] = Module[{k = 2}, While[! FreeQ[Array[a, n - 1], k] || ! StringContainsQ[ToString[a[n - 1] + k], ToString[n - 1]], k++]; k]; Array[a, 100] (* _Amiram Eldar_, Jul 04 2023 *)

%Y Cf. A299952.

%K base,nonn

%O 1,2

%A _Eric Angelini_, Jul 03 2023