A241175 -id:A241175 - 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.

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

David Consiglio, Jr., May 13 2014

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.

			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.)

Cf. A241175.

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)

A332677 a(n) is the number of ways n can be obtained by adding some digit of a number k to k.

Original entry on oeis.org

1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 1, 3, 1, 3, 1, 3, 1, 3, 0, 3, 1, 2, 1, 3, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 3, 0, 3, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 3, 1, 2, 1, 3, 1, 3, 0, 3, 1, 3, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 3, 1, 3, 1, 2, 1, 3, 0

Offset: 0

Giovanni Resta, Feb 19 2020

By definition terms cannot exceed 10. The values from 0 to 10 are obtained the first time with n = 1, 0, 10, 14, 102, 104, 1206, 12406, 124506, 1245606, and 12456806, respectively.

			a(102) = 4 because 102 can written as 93+9, 96+6, 101+1, and 102+0.

Eric Angelini, Posting to Sequence Fans Mailing List, Apr 20 2014.

Cf. A241175, A241176, A241177, A241178, A241179.

a[n_] := Sum[ Boole[ MemberQ[ IntegerDigits[t] + t, n]], {t, Max[0, n-9], n}]; Array[a, 88, 0]

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.

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