A137564 - OEIS

%I #43 Mar 22 2024 18:42:56

%S 0,1,2,3,4,5,6,7,8,9,10,1,12,13,14,15,16,17,18,19,20,21,2,23,24,25,26,

%T 27,28,29,30,31,32,3,34,35,36,37,38,39,40,41,42,43,4,45,46,47,48,49,

%U 50,51,52,53,54,5,56,57,58,59,60,61,62,63,64,65,6,67,68,69,70,71,72,73,74,75,76,7,78,79,80,81,82,83,84,85,86,87,8,89,90,91,92,93,94,95,96,97,98,9,10,10,102,103,104,105,106,107,108,109,10,1,12

%N a(n) is the number formed by removing from n all duplicate digits except the leftmost copy of each.

%C Differs from A106612: a(100) = 10, A106612(100) = 100.

%C Differs from A337864: a(101) = 10, A337864(101) = 101.

%C a(n)=n iff n is a term of A010784. a(n)<n iff n is a term of A109303.

%C A010784 is the sequence of distinct terms in this sequence, thus 9876543210 is the largest term here also, as no digit occurs more than once in any given term. Each term except 0 appears infinitely often in this sequence. - _Rick L. Shepherd_, Oct 03 2020

%H Reinhard Zumkeller, <a href="/A137564/b137564.txt">Table of n, a(n) for n = 0..10000</a> (corrected by Andrew Howroyd at the suggestion of Rodolfo Kurchan and Omar E. Pol, Oct 04 2020)

%e a(100)=10 as a (second) 0 digit is dropped. a(1211323171)=1237.

%e a(10...1) = 10 for any number of 0's and/or 1's in any order replacing the "..." in the term's index. - _Rick L. Shepherd_, Oct 03 2020

%t Table[FromDigits@ DeleteDuplicates@ IntegerDigits@ n, {n, 74}] (* _Michael De Vlieger_, Jun 01 2016 *)

%o (PARI) a(n)={my(d=digits(n)); fromdigits(vecextract(d, vecsort(vecsort(d,,9))))} \\ _Andrew Howroyd_, Oct 04 2020

%o (Perl) sub a {my($n)=@_; my @seen; $n =~ s{.}{!$seen[$&]++ && $&}eg; $n} # _Kevin Ryde_, Oct 04 2020

%o (Python)

%o def a(n):

%o     seen, out, s = set(), "", str(n)

%o     for d in s:

%o         if d not in seen: out += d; seen.add(d)

%o     return int(out)

%o print([a(n) for n in range(113)]) # _Michael S. Branicky_, Jul 23 2022

%Y Cf. A106612, A010784 (fixed points), A109303 (non-fixed).

%Y Cf. A043529 (equivalent in binary, except at n=0), A337864.

%K base,easy,nonn

%O 0,3

%A _Rick L. Shepherd_, Jan 25 2008