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A125289 Numbers with unique nonzero digit in decimal representation.

%I A125289 #18 Mar 14 2025 16:05:30
%S A125289 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,
%T A125289 99,100,101,110,111,200,202,220,222,300,303,330,333,400,404,440,444,
%U A125289 500,505,550,555,600,606,660,666,700,707,770,777,800,808,880,888,900,909
%N A125289 Numbers with unique nonzero digit in decimal representation.
%C A125289 A043537(a(n)) <= 2.
%C A125289 A043537(A004719(a(n))) = 1: A004719(a(n)) is a repdigit number, see A010785;
%C A125289 also numbers having exactly one partition into digit values of their decimal representations: A061827(a(n))=1.
%H A125289 Rémy Sigrist, <a href="/A125289/b125289.txt">Table of n, a(n) for n = 1..9207</a>
%H A125289 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RepeatingDecimal.html">Repeating Decimal</a>
%H A125289 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repdigit.html">Repdigit</a>
%o A125289 (Python)
%o A125289 A125289_list = [n for n in range(10**4) if len(set(str(n))-{'0'})==1]
%o A125289 # _Chai Wah Wu_, Jan 04 2015
%o A125289 (Python)
%o A125289 from itertools import count, product, islice
%o A125289 def A125289_gen(): # generator of terms
%o A125289     yield from (int(d+''.join(m)) for l in count(0) for d in '123456789' for m in product('0'+d,repeat=l))
%o A125289 A125289_list = list(islice(A125289_gen(),20)) # _Chai Wah Wu_, Mar 14 2025
%o A125289 (PARI) is(n, base=10) = #Set(select(sign, digits(n, base)))==1 \\ _Rémy Sigrist_, Mar 28 2020
%o A125289 (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
%Y A125289 Cf. A125292.
%K A125289 nonn,base
%O A125289 1,2
%A A125289 _Reinhard Zumkeller_, Nov 26 2006