cp's OEIS Frontend

A242437 Numbers not appearing in the sequence of integers, beginning with 1, that can be formed by adding any digit of any previous term to that previous term.

%I A242437 #15 May 22 2025 10:21:37
%S A242437 3,5,6,7,9,10,11,12,13,14,15,21,23,25,27,29,31,43,47,51,65,71,87,95
%N A242437 Numbers not appearing in the sequence of integers, beginning with 1, that can be formed by adding any digit of any previous term to that previous term.
%C A242437 Is this sequence finite?  Any additional term > 10^8.
%C A242437 If we start with an integer other than 1, different sequences appear.  3, 5, and 7 appear in none of these sequences starting with any n less than the integer in question.  Are there any other integers, like 3, 5, and 7, that do not appear in any sequence starting with n less than the integer in question?
%C A242437 This sequence includes all terms from A241175 plus additional terms that cannot be made from the terms that are included in A241175.
%e A242437 17 is not in this sequence because 1+1=2, 2+2=4, 4+4=8, 8+8=16, 16+1=17.
%e A242437 39 is not in this sequence because 1+1=2, 2+2=4, 4+4=8, 8+8=16, 16+6=22, 22+2=24, 24+4=28, 28+8=36, 36+3=39.
%e A242437 23 is in this sequence because there is no way to start at 1 and arrive at 23.
%e A242437 (See A241175 for definition difference.)
%o A242437 (Python)
%o A242437 complete = []
%o A242437 complete.append(1)
%o A242437 complete.append(2)
%o A242437 complete.append(4)
%o A242437 complete.append(8)
%o A242437 final = []
%o A242437 for a in range(2,10000000):#search through 10^8
%o A242437     b = str(a)
%o A242437     for c in reversed(range(1,10)):#search the previous 9 integers
%o A242437         d = str(a-c)
%o A242437         if a - c in complete[-9:] and str(c) in d:
%o A242437             complete.append(a)#this number can be made by digit addition
%o A242437             break
%o A242437         if c == 1:#If all 9 attempts fail
%o A242437             final.append(a)#This is a member of the new sequence
%o A242437 print(final)
%Y A242437 Cf. A241175.
%K A242437 nonn,easy,base
%O A242437 1,1
%A A242437 _David Consiglio, Jr._, May 13 2014