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

1,1

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.

Links

Table of n, a(n) for n=1..24.

Example

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.)

Prog

(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)

Crossrefs

Cf. A241175.

Sequence in context: A308468 A213199 A184987 * A370301 A188916 A276278

Adjacent sequences: A242434 A242435 A242436 * A242438 A242439 A242440

Keyword

nonn,easy,base

Author

David Consiglio, Jr., May 13 2014

Status

approved