A054659 Increasing sequence with no repeating digits and no digits shared with previous term.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 40, 51, 60, 71, 80, 91, 203, 415, 602, 713, 802, 913, 2045, 3167, 4025, 6137, 8024, 9135, 20467, 31589, 40267, 51389, 60247, 81359

Offset: 1

Author

Henry Bottomley, Apr 18 2000

Keywords

• nonn
• base
• easy
• fini
• full

Comments

a(11)=23 since a(10)=10 and any number from 11 to 21 would share a digit between the two terms while 22 has a repeated digit

Crossrefs

Cf. A030283.

Programs

Python

def ok(s, t): return len(set(t)) == len(t) and len(set(s+t)) == len(s+t)
def agen(): # generator of complete sequence of terms
    an, MAX = 0, 987654321
    while True:
        if an < MAX: yield an
        else: return
        an, s = an+1, str(an)
        MAX = 10**(10-len(s))
        while an < MAX and not ok(s, str(an)): an += 1
print(list(agen())) # Michael S. Branicky, Jun 30 2022