A064809 -id:A064809 - cp's OEIS frontend

A228595 Lexicographically earliest sequence of distinct positive integers such that the concatenation of the terms equals the concatenation of the positive integers, and no term appears in its natural position.

12, 34, 56, 78, 910, 1, 11, 2, 131, 4, 151, 6, 171, 8, 1920, 212, 22, 3, 242, 5, 262, 7, 282, 9, 303, 13, 23, 33, 43, 53, 63, 73, 83, 940, 414, 24, 344, 454, 64, 74, 84, 950, 515, 25, 35, 45, 55, 65, 75, 85, 960, 616, 26, 36, 46, 566, 676, 86, 970, 717, 27

Offset: 1

Paul Tek, Aug 27 2013

Leading zeros are forbidden.

For any n>0, the concatenation of the (n-1) first terms never equals the concatenation of the (a(n)-1) first positive integers.

			The positive integers:
+-+-+-+-+-+-+-+-+-+---+---+---+---+---+---+---+---+---+
|1|2|3|4|5|6|7|8|9|1 0|1 1|1 2|1 3|1 4|1 5|1 6|1 7|1 8| ...
+-+-+-+-+-+-+-+-+-+---+---+---+---+---+---+---+---+---+
This sequence:
+---+---+---+---+-----+-+---+-+-----+-+-----+-+-----+-+
|1 2|3 4|5 6|7 8|9 1 0|1|1 1|2|1 3 1|4|1 5 1|6|1 7 1|8| ...
+---+---+---+---+-----+-+---+-+-----+-+-----+-+-----+-+

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, PERL program for this sequence

Cf. A033307, A064809, A098067, A197124.

Perl
```
See Link section.
```

A175728 Decimal expansion of e written as a sequence of distinct positive integers.

Original entry on oeis.org

2, 7, 1, 8, 28, 18, 284, 5, 90, 4, 52, 3, 53, 60, 287, 47, 13, 526, 6, 24, 9, 77, 57, 2470, 93, 69, 99, 59, 574, 96, 696, 76, 27, 72, 40, 766, 30, 35, 354, 75, 94, 571, 38, 21, 78, 525, 16, 64, 274, 2746, 63, 91, 93200, 305, 992, 181, 74, 135, 966, 290, 43, 572, 900, 33, 42

Offset: 1

Jason G. Wurtzel, Aug 19 2010

Inverse: 3, 1, 12, 10, 8, 19, 2, 4, 21, 119, 86, 166, 17, 154, 160, 47, 192, 6, 83, 214, ..., . - Robert G. Wilson v, Aug 22 2010

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A001113, A064809.

rd = RealDigits[E, 10, 200][[1]]; lst = {}; f[n_] := Block[{k = 1}, While[a = FromDigits[ Take[ rd, k]]; MemberQ[lst, a] || rd[[k + 1]] == 0, k++ ]; AppendTo[ lst, a]; rd = Drop[rd, k]]; Array[f, 70]; lst (* Robert G. Wilson v, Aug 22 2010 *)

from itertools import islice
from sympy import exp
def diggen():
    yield from map(int, str(exp(1).n(10**5))[:-1].replace(".", ""))
def agen(): # generator of terms
    g = diggen()
    aset, nextd = set(), next(g)
    while True:
        an, nextd = nextd, next(g)
        while an in aset or nextd == 0:
            an, nextd = int(str(an) + str(nextd)), next(g)
        yield an
        aset.add(an)
print(list(islice(agen(), 65))) # Michael S. Branicky, Mar 31 2022

More terms from Robert G. Wilson v, Aug 22 2010

cp's OEIS Frontend

A228595 Lexicographically earliest sequence of distinct positive integers such that the concatenation of the terms equals the concatenation of the positive integers, and no term appears in its natural position.

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