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?
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
KEYWORD
nonn,easy,base
AUTHOR
David Consiglio, Jr., May 13 2014
STATUS
approved