A252481 Numbers whose set of digits is simply connected to 1.

1, 10, 11, 12, 21, 100, 101, 102, 110, 111, 112, 120, 121, 122, 123, 132, 201, 210, 211, 212, 213, 221, 231, 312, 321, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1023, 1032, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1123, 1132, 1200, 1201, 1202, 1203, 1210, 1211, 1212, 1213, 1220, 1221, 1222, 1223

Offset: 1

Author

M. F. Hasler, Dec 24 2014

Keywords

• nonn
• base

Comments

"Simply connected" means that there must not be a "hole" in the set of digits. E.g., {1,2,4} would not be allowed since '3' is missing.

Crossrefs

Cf. A032981, A050278, A033075, A010785, A108965, A134336, A252490.

Programs

PARI

is(n)={d=Set(digits(n));d[1]==1 || (#d>1&&d[2]==1) || return; d[#d]==#d-!d[1]}

Python

def ok(n):
  s = set(str(n)); return '1' in s and len(s) == ord(max(s))-ord(min(s))+1
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(1223)) # Michael S. Branicky, Jan 10 2021