A297065 -id:A297065 - cp's OEIS frontend

A362075 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-2) + a(n-1).

1, 2, 4, 3, 5, 6, 7, 8, 9, 20, 10, 11, 30, 22, 13, 12, 14, 15, 16, 24, 17, 23, 18, 25, 19, 21, 26, 28, 27, 29, 31, 32, 40, 33, 41, 35, 34, 37, 36, 42, 39, 43, 44, 45, 46, 38, 50, 47, 48, 60, 49, 52, 53, 62, 63, 64, 54, 55, 56, 57, 58, 66, 59, 67, 70, 65, 68, 69, 80, 72, 73, 76, 75, 74, 77, 78

Offset: 1

Scott R. Shannon, Apr 08 2023

The sequence is likely to be finite although it contains at least 100000 terms.

Sequence is finite with 4128755 terms, since a(4128754) = 46946449 and a(4128755) = 777000707 have sum 823947156. - Michael S. Branicky, Apr 08 2023

			a(10) = 20 as a(8) + a(9) = 8 + 9 = 17, and 20 is the smallest unused number that does not contain the digits 1 or 7.

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Michael S. Branicky, Python program
Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Cf. A362076, A342441, A342442, A067581, A297065.

# see linked program that generates the full sequence

A362093 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-1) - a(n-2).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 22, 10, 30, 11, 23, 33, 24, 12, 34, 13, 35, 14, 36, 15, 37, 16, 38, 17, 39, 18, 40, 19, 43, 31, 44, 25, 26, 27, 28, 29, 32, 21, 42, 45, 41, 50, 46, 51, 47, 52, 48, 53, 49, 55, 54, 56, 57, 58, 59, 60, 62, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 71, 73, 74, 75, 76, 77

Offset: 1

Scott R. Shannon, Apr 08 2023

nonn

The sequence is likely to be finite although it contains at least 1 million terms.

Sequence is finite with 6080472 terms, since a(6080471) = 660606060 and a(6080472) = 8822811 have difference -651783249. - Michael S. Branicky, Apr 09 2023

			a(11) = 22 as a(10) - a(9) = 20 - 9 = 11, and 22 is the smallest unused number that does not contain the digit 1.

Michael S. Branicky, Python program
Scott R. Shannon, Image of the first 1 million terms. The green line is a(n) = n.

Cf. A362075, A362076, A342441, A342442, A067581, A297065.

# see link for program that generates full sequence

A362076 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-2) * a(n-1).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 13, 14, 30, 15, 12, 23, 18, 20, 17, 16, 19, 21, 24, 26, 31, 25, 28, 29, 33, 32, 27, 35, 36, 34, 37, 39, 50, 38, 42, 40, 43, 44, 45, 46, 41, 47, 48, 49, 60, 51, 52, 70, 55, 61, 62, 54, 56, 57, 58, 59, 65, 64, 53, 66, 67, 63, 68, 69, 71, 72, 73, 74, 76, 77

Offset: 1

Scott R. Shannon, Apr 08 2023

The sequence is finite; after 6481 terms a(6480) = 5211 and a(6481) = 44444 resulting in a product of 5211 * 44444 = 231597684. This contains all digits 1 to 9 so the next term does not exist.

The sequence contains 40 fixed points, the last being a(5477).

			a(12) = 22 as a(10) * a(11) = 10 * 11 = 110, and 22 is the smallest unused number that does not contain the digits 0 or 1.

Michael S. Branicky, Table of n, a(n) for n = 1..6481
Michael S. Branicky, Python program
Scott R. Shannon, Image of the 6481 terms. The green line is a(n) = n.

Cf. A362075, A342441, A342442, A067581, A297065.

Python
```
# see linked program
```

A107411 Each digit of a(n) appears in a(n+1) and a(n+1) > a(n) is minimal.

Original entry on oeis.org

0, 10, 100, 101, 102, 120, 201, 210, 1002, 1012, 1020, 1021, 1022, 1023, 1032, 1203, 1230, 1302, 1320, 2013, 2031, 2103, 2130, 2301, 2310, 3012, 3021, 3102, 3120, 3201, 3210, 10023, 10032, 10123, 10132, 10203, 10213, 10223, 10230, 10231, 10232, 10233, 10234, 10243

Offset: 0

Eric Angelini, Jun 09 2005

Starting with another integer as 0 (the "seed") would lead to another sequence.

			After 100 we get 101 (and not 1000) because the lone 0 in "101" is considered as the copy of both zeros of "100".

Michael S. Branicky, Table of n, a(n) for n = 0..10000

Cf. A297065.

R:= 0: S:= {0}: count:= 1;
for k from 1 while count < 100 do
  Sk:= convert(convert(k,base,10),set);
  if S subset Sk then
    R:= R, k;
    count:= count+1;
    S:= Sk;
  fi
od:
R; # Robert Israel, Nov 21 2022

from itertools import islice
def agen(an=0):
    while True:
        yield an
        target, k = set(str(an)), an + 1
        while not (target <= set(str(k))): k += 1
        an = k
print(list(islice(agen(), 41))) # Michael S. Branicky, Nov 21 2022

Missing terms a(35)-a(37) inserted by Michael S. Branicky, Nov 21 2022

cp's OEIS Frontend

A362075 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-2) + a(n-1).

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A362093 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-1) - a(n-2).

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A362076 a(1) = 1, a(2) = 2; for n > 2, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-2) * a(n-1).

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A107411 Each digit of a(n) appears in a(n+1) and a(n+1) > a(n) is minimal.

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