A276512 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-2); a(0)=0, a(1)=1.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 20, 13, 14, 24, 23, 15, 16, 26, 25, 17, 18, 28, 27, 19, 30, 32, 12, 40, 33, 21, 29, 34, 31, 50, 42, 36, 35, 41, 44, 37, 38, 45, 46, 39, 51, 47, 43, 52, 55, 48, 49, 53, 56, 60, 70, 54, 58, 61, 62, 57, 59, 63, 64, 71, 72, 65, 66, 73, 74, 68, 69, 75

Offset

0,3

Comments

This is not a permutation of the nonnegative integers. E.g. 123456789 and 1023456789 (the smallest pandigital number) are not members.

a(n) = n for n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 34, 84, 104, 105, 1449, 2889, 3183, ...

Links

Zak Seidov, Table of n, a(n) for n = 0..5000

Mathematica

s={0, 1}; Do[a=s[[-2]]; n=2; While[MemberQ[s, n]||Intersection [IntegerDigits[a], IntegerDigits[n]]≠{}, n++]; AppendTo[s, n], {100}]; s

Prog

(Python)
from itertools import count, islice, product as P
def only(s, D=1): # numbers with >= D digits only from s
    yield from (int("".join(p)) for d in count(D) for p in P(s, repeat=d))
def agen(): # generator of terms
    aset, an1, an, minan = {0, 1}, 0, 1, 2
    yield from [0, 1]
    while True:
        an1, an, s = an, minan, set(str(an1))
        use = "".join(c for c in "0123456789" if c not in s)
        for an in only(use, D=len(str(minan))):
            if an not in aset: break
        aset.add(an)
        yield an
        while minan in aset: minan += 1
print(list(islice(agen(), 75))) # Michael S. Branicky, Jun 30 2022

Crossrefs

Cf. A054659, A067581, A276633, A276766.

Sequence in context: A004186 A034704 A362076 * A023792 A221221 A355224

Adjacent sequences: A276509 A276510 A276511 * A276513 A276514 A276515

Keyword

nonn,base

Author

Zak Seidov and Eric Angelini, Sep 06 2016

Status

approved