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

0,3

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)<n iff n is a term of 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

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)

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

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

Sequence in context: A321802 A337864 A106612 * A056960 A227362 A297236

Adjacent sequences: A137561 A137562 A137563 * A137565 A137566 A137567

Keyword

base,easy,nonn

Author

Rick L. Shepherd, Jan 25 2008

Status

approved