A029740 Odd numbers with distinct digits.

1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 103, 105, 107, 109, 123, 125, 127, 129, 135, 137, 139, 143, 145, 147, 149, 153, 157

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• fini
• base

Comments

The sequence has 4384045 terms. - Harvey P. Dale, Jan 12 2019

Maximum term is 9876543201. Next higher number with distinct digits is 9876543210. - Alonso del Arte, Jan 09 2020

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Patrick De Geest, World!Of Numbers

Crossrefs

Cf. A029741 (even version). Union of that sequence with this sequence gives A010784.

Programs

Mathematica

Select[Range[1, 199, 2], Max[DigitCount[#]] == 1 &] (* Harvey P. Dale, Jan 12 2019 *)

Python

# generates full sequence
from itertools import permutations
afull = sorted(set(int("".join(p)) for d in range(1, 11) for p in permutations("0123456789", d) if p[0] != "0" and p[-1] in "13579"))
print(afull[:100]) # Michael S. Branicky, Aug 04 2022

Scala

def hasDistinctDigits(n: Int): Boolean = {
  val numerStr = n.toString
  val digitSet = numerStr.split("").toSet
  numerStr.length == digitSet.size
}
(1 to 199 by 2).filter(hasDistinctDigits) // Alonso del Arte, Jan 09 2020

Extensions

First comment corrected by Harvey P. Dale, Mar 04 2020 at the insistence of Sean A. Irvine

Offset changed to 1 by Michael S. Branicky, Aug 04 2022

Removed incorrect Sage program. - N. J. A. Sloane, Aug 04 2022