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.

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 21, 23, 25, 27, 29, 31, 43, 47, 51, 65, 71, 87, 95

Offset: 1

Author

David Consiglio, Jr., May 13 2014

Keywords

• nonn
• easy
• base

Comments

Is this sequence finite? Any additional term > 10^8.

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?

This sequence includes all terms from A241175 plus additional terms that cannot be made from the terms that are included in A241175.

Examples

			17 is not in this sequence because 1+1=2, 2+2=4, 4+4=8, 8+8=16, 16+1=17.
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.
23 is in this sequence because there is no way to start at 1 and arrive at 23.
(See A241175 for definition difference.)
		

Crossrefs

Cf. A241175.

Programs

Python

complete = []
complete.append(1)
complete.append(2)
complete.append(4)
complete.append(8)
final = []
for a in range(2,10000000):#search through 10^8
    b = str(a)
    for c in reversed(range(1,10)):#search the previous 9 integers
        d = str(a-c)
        if a - c in complete[-9:] and str(c) in d:
            complete.append(a)#this number can be made by digit addition
            break
        if c == 1:#If all 9 attempts fail
            final.append(a)#This is a member of the new sequence
print(final)