A137564 a(n) is the number formed by removing from n all duplicate digits except the leftmost copy of each.

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

Offset: 0

Author

Rick L. Shepherd, Jan 25 2008

Keywords

• base
• easy
• nonn

Comments

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

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

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

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 (corrected by Andrew Howroyd at the suggestion of Rodolfo Kurchan and Omar E. Pol, Oct 04 2020)

Crossrefs

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

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

Programs

Mathematica

Table[FromDigits@ DeleteDuplicates@ IntegerDigits@ n, {n, 74}] (* Michael De Vlieger, Jun 01 2016 *)

PARI

a(n)={my(d=digits(n)); fromdigits(vecextract(d, vecsort(vecsort(d,,9))))} \\ Andrew Howroyd, Oct 04 2020

Perl

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

Python

def a(n):
    seen, out, s = set(), "", str(n)
    for d in s:
        if d not in seen: out += d; seen.add(d)
    return int(out)
print([a(n) for n in range(113)]) # Michael S. Branicky, Jul 23 2022