A370400 Lexicographically earliest sequence of distinct nonnegative terms such that the last digit of a(n) is present in a(n+1).

0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 101, 1, 11, 12, 2, 21, 13, 3, 23, 31, 14, 4, 24, 34, 41, 15, 5, 25, 35, 45, 51, 16, 6, 26, 36, 46, 56, 61, 17, 7, 27, 37, 47, 57, 67, 71, 18, 8, 28, 38, 48, 58, 68, 78, 81, 19, 9, 29, 39, 49, 59, 69, 79, 89, 91, 102, 22, 32, 42, 52, 62, 72, 82, 92, 112, 120, 103, 33

Offset

1,2

Comments

This is not A156819.

Links

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

Eric Angelini, Talking to me?, personal blog, Feb 2024.

Example

a(12) = 101 and the rightmost digit "1" is present in the next term ( 1)
a(13) =   1 and the rightmost digit "1" is present in the next term (11)
a(14) =  11 and the rightmost digit "1" is present in the next term (12)
a(15) =  12 and the rightmost digit "2" is present in the next term ( 2)
a(16) =   2 and the rightmost digit "2" is present in the next term (21)
a(17) =  21 and the rightmost digit "1" is present in the next term (13), etc.

Mathematica

a[1]=0; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n-1], k]|| FreeQ[IntegerDigits@k, Mod[a[n-1], 10]], k++]; k); Array[a, 79]

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    an, aset, mink = 0, set(), 1
    while True:
        yield an
        aset.add(an)
        t, k = str(an%10), mink
        an = next(k for k in count(mink) if k not in aset and t in str(k))
        while mink in aset: mink += 1
print(list(islice(agen(), 79))) # Michael S. Branicky, Feb 18 2024

Crossrefs

Cf. A370401, A370402, A370403, A370404, A370405, A156819.

Sequence in context: A338641 A337857 A044895 * A156819 A139079 A360443

Adjacent sequences: A370397 A370398 A370399 * A370401 A370402 A370403

Keyword

base,nonn

Author

Eric Angelini and Giorgos Kalogeropoulos, Feb 17 2024

Status

approved