A125289 Numbers with unique nonzero digit in decimal representation.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 22, 30, 33, 40, 44, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99, 100, 101, 110, 111, 200, 202, 220, 222, 300, 303, 330, 333, 400, 404, 440, 444, 500, 505, 550, 555, 600, 606, 660, 666, 700, 707, 770, 777, 800, 808, 880, 888, 900, 909

Offset: 1

Author

Reinhard Zumkeller, Nov 26 2006

Keywords

• nonn
• base

Comments

A043537(a(n)) <= 2.

A043537(A004719(a(n))) = 1: A004719(a(n)) is a repdigit number, see A010785;

also numbers having exactly one partition into digit values of their decimal representations: A061827(a(n))=1.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..9207
• Eric Weisstein's World of Mathematics, Repeating Decimal
• Eric Weisstein's World of Mathematics, Repdigit

Crossrefs

Cf. A125292.

Programs

PARI

is(n, base=10) = #Set(select(sign, digits(n, base)))==1 \\ Rémy Sigrist, Mar 28 2020

PARI

a(n,base=10) = { for (w=0, oo, if (n<=(base-1)*2^w, my (d=1+(n-1)\2^w, k=2^w+(n-1)%(2^w)); return (d*fromdigits(binary(k), base)), n -= (base-1)*2^w)) } \\ Rémy Sigrist, Mar 28 2020

Python

A125289_list = [n for n in range(10**4) if len(set(str(n))-{'0'})==1]
# Chai Wah Wu, Jan 04 2015

Python

from itertools import count, product, islice
def A125289_gen(): # generator of terms
    yield from (int(d+''.join(m)) for l in count(0) for d in '123456789' for m in product('0'+d,repeat=l))
A125289_list = list(islice(A125289_gen(),20)) # Chai Wah Wu, Mar 14 2025