A320486 Keep just the digits of n that appear exactly once; write 0 if all digits disappear.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 0, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 0, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 0, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 0, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 0, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 0, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 0, 1, 0, 102, 103, 104, 105, 106, 107, 108, 109, 0, 0, 2, 3, 4, 5, 6, 7, 8, 9, 120, 2, 1, 123, 124, 125, 126, 127, 128, 129, 130, 3

Offset

0,3

Comments

Digits that appear more than once in n are erased. Leading zeros are erased unless the result is 0. If all digits are erased, we write 0 for the result (A320485 is another version, which uses -1 for the empty string).

More than the usual number of terms are shown in order to reach some interesting examples.

a(n) = 0 mostly. - David A. Corneth, Oct 24 2018

The number of d-digit numbers n for which a(n) > 0 is at most d*9^d, so in this sense most a(n) are 0. - Robert Israel, Oct 24 2018

The set of numbers with the property that their digits appear at least twice is of asymptotic density 1 (and the set of numbers that have a digit that occurs only once is of density 0), so in that sense it is rather exceptional for large n to have a(n) > 0. - M. F. Hasler, Oct 24 2018

References

Eric Angelini, Posting to Sequence Fans Mailing List, Oct 24 2018

Links

Robert Israel, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

Example

1231 becomes 23, 1123 becomes 23, 11231 becomes 23, and 11023 becomes 23 (as we don't accept leading zeros). Note that 112323 disappears immediately and we get 0.
101, 110, 11000, 10001 all become 0.

Maple

f:= proc(n) local F, S;
  F:= convert(n, base, 10);
  S:= select(t -> numboccur(t, F)>1, [$0..9]);
  if S = {} then return n fi;
  F:= subs(seq(s=NULL, s=S), F);
  add(F[i]*10^(i-1), i=1..nops(F))
end proc:
map(f, [$0..200]); # Robert Israel, Oct 24 2018

Mathematica

Table[If[(c=Select[b=IntegerDigits[n], Count[b, #]==1&])=={}, 0, FromDigits@c], {n, 0, 131}] (* Giorgos Kalogeropoulos, May 09 2021 *)
d1[n_]:=Module[{idn=IntegerDigits[n]}, FromDigits[If[DigitCount[n, 10, #]>1, Nothing, #]&/@ idn]]; Array[d1, 150, 0] (* Harvey P. Dale, Jun 23 2023 *)

Prog

(PARI) a(n) = {my(d=digits(n), v = vector(10), res = 0); for(i=1, #d, v[d[i]+1]++); for(i=1, #d, if(v[d[i]+1]==1, res=10*res+d[i])); res}
(PARI) A320486(n, D=digits(n))=fromdigits(select(d->#select(t->t==d, D)<2, D)) \\ M. F. Hasler, Oct 24 2018
(Python)
def A320486(n):
    return int('0'+''.join(d if str(n).count(d) == 1 else '' for d in str(n))) # Chai Wah Wu, Nov 19 2018

Crossrefs

See A320485 for a different version.

Cf. A321008-A321012, A321021.

Sequence in context: A259434 A329079 A306580 * A321801 A278946 A322629

Adjacent sequences: A320483 A320484 A320485 * A320487 A320488 A320489

Keyword

nonn,base,look

Author

N. J. A. Sloane, Oct 24 2018

Status

approved