A337864 -id:A337864 - cp's OEIS frontend

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

Rick L. Shepherd, Jan 25 2008

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

			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

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)

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

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

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

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

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

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

A356014 Consider the exponents in the prime factorization of n, and replace each run of k consecutive e's by a unique e; the resulting list corresponds to the exponents in the prime factorization of a(n).

Original entry on oeis.org

1, 2, 3, 4, 3, 2, 3, 8, 9, 10, 3, 12, 3, 10, 3, 16, 3, 18, 3, 20, 21, 10, 3, 24, 9, 10, 27, 20, 3, 2, 3, 32, 21, 10, 3, 4, 3, 10, 21, 40, 3, 10, 3, 20, 45, 10, 3, 48, 9, 50, 21, 20, 3, 54, 21, 40, 21, 10, 3, 12, 3, 10, 63, 64, 21, 10, 3, 20, 21, 10, 3, 72, 3

Offset: 1

Rémy Sigrist, Jul 23 2022

nonn

We ignore the exponents (all 0's) for the prime numbers beyond the greatest prime factor of n.

This sequence operates on prime exponents as A090079 and A337864 operate on binary and decimal digits, respectively.

			For n = 99:
- 99 = 11^1 * 7^0 * 5^0 * 3^2 * 2^0,
- the list of exponents is: 1 0 0 2 0,
- compressing consecutive values, we obtain: 1 0 2 0,
- so a(99) = 7^1 * 5^0 * 3^2 * 2^0 = 63.

Cf. A007814, A061742, A067255, A090079, A115964, A294674, A319521, A337864, A356008, A356021 (fixed points).

a(n) = { my (v=1, e=-1, k=0); forprime (p=2, oo, if (n==1, return (v), if (e!=e=valuation(n,p), v*=prime(k++)^e); n/=p^e)) }

a(a(n)) = a(n).
a(n^k) = a(n)^k for any k >= 0.
a(n) = A319521(A356008(n)).
A007814(a(n)) = A007814(n).
a(n) = 3 iff n belongs to A294674 \ {1}.
a(n) = 4 iff n belongs to A061742 \ {1}.
a(n) = 8 iff n belongs to A115964.

cp's OEIS Frontend

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

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