A357377 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that |a(n) - a(n-1)| does not appear in the string concatenation of a(0)..a(n-1).

0, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25, 2, 6, 10, 14, 22, 4, 12, 20, 28, 44, 8, 24, 40, 56, 18, 34, 50, 23, 39, 55, 26, 42, 58, 29, 45, 61, 31, 47, 63, 27, 43, 59, 75, 37, 53, 69, 85, 36, 52, 68, 30, 46, 62, 78, 94, 110, 33, 49, 65, 81, 97, 113, 41, 57, 73, 35, 51, 67, 105, 143, 16, 54

Offset

0,3

Comments

The sequence is conjectured to be a permutation of the positive integers. In the first 200000 terms the only fixed points are 20, 24, 43 and 115. It is likely no more exist although this is unknown.

There are no other fixed points in the first 870000 terms. - Michael S. Branicky, Oct 05 2022

Links

Table of n, a(n) for n=0..74.

Scott R. Shannon, Image for n=0..200000. The green line is a(n) = n.

Example

a(12) = 25 as the concatenation of a(0)..a(11) is "013579111315171921" and |25 - a(11)| = |25 - 21| = 4 which does not appear in the concatenated string. Since a(11) contains a '2' and all other odd numbers appear in the string a(12) cannot be 23 or any even number less than 25.
a(13) = 2 as the concatenation of a(0)..a(12) is "01357911131517192125" and |2 - a(12)| = |2 - 25| = 23 which does not appear in the concatenated string.

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    alst, aset, astr, an, mink, mindiff = [], set(), "", 0, 1, 1
    for n in count(0):
        yield an; aset.add(an); astr += str(an)
        prevan, an = an, mink
        while an + mindiff <= prevan and (an in aset or str(abs(an-prevan)) in astr): an += 1
        if an in aset or str(abs(an-prevan)) in astr:
            an = max(mink, prevan + mindiff)
            while an in aset or str(an-prevan) in astr:
                an += 1
        while mink in aset: mink += 1
        while str(mindiff) in astr: mindiff += 1
print(list(islice(agen(), 75))) # Michael S. Branicky, Oct 05 2022

Crossrefs

Cf. A355611 (base 2), A357082, A007088, A030302, A118248, A341766.

Sequence in context: A246411 A158333 A293167 * A062505 A230104 A093031

Adjacent sequences: A357374 A357375 A357376 * A357378 A357379 A357380

Keyword

nonn,base,look

Author

Scott R. Shannon, Sep 26 2022

Status

approved