A382462 Lexicographically earliest sequence of distinct positive integers such that if a digit d in the digit stream (ignoring commas) is even, the previous digit is < d.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 31, 21, 23, 33, 34, 35, 36, 37, 38, 39, 51, 24, 53, 41, 25, 55, 56, 57, 58, 59, 71, 26, 73, 43, 45, 61, 27, 75, 63, 46, 77, 78, 79, 91, 28, 93, 47, 81, 29, 95, 65, 67, 83, 48, 97, 85, 68, 99, 111, 49, 112, 69

Offset: 1

Author

Paolo Xausa, Mar 27 2025

Keywords

• nonn
• base
• look

Comments

Could be summarized as "even digit, previous smaller". A variant of A342042.

No term contains the digit 0. - Paolo Xausa, Apr 30 2025

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Similar sequences: A342042, A342043, A342044, A342045, A382621, A382935, A383059.

Cf. A382463, A382464, A382465, A382466.

Programs

Mathematica

A382462list[nmax_] := Module[{a, s, invQ, fu = 2},
  invQ[k_] := invQ[k] = (If[#, s[k] = #]; #) & [MemberQ[Partition[IntegerDigits[k], 2, 1], {i_, j_?EvenQ} /; i >= j]];
  s[_] := False; s[1] = True;
  NestList[(a = fu; While[s[a] || invQ[a] || invQ[# + First[IntegerDigits[a]]], a++] & [Mod[#, 10]*10]; While[s[fu], fu++]; s[a] = True; a) &, 1, nmax-1]];
A382462list[100]

Python

from itertools import count, islice
def cond(s):
    return all(s[i] > s[i-1] for i in range(1, len(s)) if s[i] in "02468")
def agen(): # generator of terms
    an, seen, s, m = 1, {1}, "1", 1
    while True:
        yield an
        an = next(k for k in count(m) if k not in seen and cond(s[-1]+str(k)))
        seen.add(an); s += str(an)
        while m in seen or not cond(str(m)): m += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Apr 19 2025