A273883 Pick any pair of "5" digits in the sequence. Those two "5"s are separated by k digits. This is the lexicographically earliest sequence of distinct terms in which all the resulting values of k are distinct.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 60, 52, 61, 62, 63, 53, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 75, 79

Offset

1,3

Comments

The sequence starts with a(1)=0. It is then always extended with the smallest integer not yet present and not leading to a contradiction (which would mean producing a value of k already seen).

Links

Eric Angelini, Table of n, a(n) for n = 1..1011

Prog

(Python)
from itertools import count, islice
def newdiffs(s, alen, locs1, diffs1):
    out = set(alen+i-j for i, c in enumerate(s, 1) if c == '5' for j in locs1)
    out |= set(i-j for j in range(len(s)-1) for i in range(j+1, len(s)) if '5' == s[i] == s[j])
    return out
def agen(): # generator of terms
    an, locs1, diffs1, mink, aset, alen = 0, [], set(), 1, {0}, 1
    while True:
        yield an
        an = next(k for k in count(mink) if k not in aset and ('5' not in (s:=str(k)) or not newdiffs(s, alen, locs1, diffs1)&diffs1))
        stran = str(an)
        if '5' in stran:
            diffs1 |= newdiffs(stran, alen, locs1, diffs1)
            locs1.extend([alen+i for i, c in enumerate(stran, 1) if c == '5'])
        alen += len(stran)
        aset.add(an)
        while mink in aset: mink += 1
print(list(islice(agen(), 74))) # Michael S. Branicky, Oct 01 2025

Crossrefs

Cf. A273376 (equivalent with digit "1").

Cf. A273880, A273881, A273882, A273884, A273885, A273886, A273887, A273888.

Sequence in context: A273058 A044922 A346447 * A132145 A272284 A322554

Adjacent sequences: A273880 A273881 A273882 * A273884 A273885 A273886

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Jun 02 2016

Status

approved