A380298 Lexicographically earliest sequence of positive integers such that any value in the sequence, say v, appears at most twice, and in case v appears twice, then the decimal expansion of v appears in the concatenation of the values surrounded by the two occurrences of v.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 11, 12, 2, 13, 3, 14, 4, 15, 5, 16, 6, 17, 7, 18, 8, 19, 9, 20, 21, 22, 12, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 13, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 14, 43, 44, 34, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 15

Offset

1,2

Comments

Every positive integer appears twice in the present sequence:

- we can always extend the sequence with a value not yet in the sequence,

- for any n > 1, a(n) is at most one plus the greatest value so far,

- every integer appears at least once in the sequence (for any v > 0, v necessarily appears at least once among the 2*v-1 initial terms),

- for any v > 0, the first occurrence of v appears before the first occurrence of v+1,

- every integer appears twice in the sequence: for any v > 0, the value 10*v appears after the first occurrence of v, so eventually v must appear a second time.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Perl program

Prog

(Perl) # See Links section.
(Python)
from itertools import count, islice
def agen(): # generator of terms
    adict, an, m, s, sn = dict(), 1, 1, "", [None]
    for n in count(1):
        yield an
        s += str(an)
        sn.append(len(s))
        adict[an] = [n] if an not in adict else adict[an] + [n]
        an = next(k for k in count(m) if k not in adict or (len(adict[k])==1 and str(k) in s[sn[adict[k][0]]:]))
        while m in adict and len(adict[m]) > 1: m += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Jan 19 2025

Crossrefs

See A380300 for a similar sequence.

Sequence in context: A373211 A346393 A389875 * A360074 A392597 A280505

Adjacent sequences: A380295 A380296 A380297 * A380299 A380300 A380301

Keyword

nonn,base

Author

Rémy Sigrist, Jan 19 2025

Status

approved