A320485 Keep just the digits of n that appear exactly once; write -1 if all digits disappear.

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

The map n -> a(n) was invented by Eric Angelini and described in a posting to the Sequence Fans Mailing List on Oct 24 2018.

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

a(n) = -1 mostly. - David A. Corneth, 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)

Formula

From Rémy Sigrist, Oct 24 2018: (Start)

a(n) = n iff n belong to A010784.

a(n) <= 9876543210 with equality iff n = 9876543210.

(End)

If n > 9876543210, then a(n) < n. If a(n) < n, then a(n) <= 99n/1000. - Chai Wah Wu, Oct 24 2018

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 -1.
101 and 110 become 0 while 11000 and 10001 become -1.

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);
  if F = [] then -1
  else add(F[i]*10^(i-1), i=1..nops(F))
  fi
end proc:
map(f, [$0..200]); # Robert Israel, Oct 24 2018

Mathematica

Array[If[# == {}, -1, FromDigits@ #] &@ Map[If[#[[-1]] > 1, -1, #[[1]] ] /. -1 -> Nothing &, Tally@ IntegerDigits[#]] &, 131] (* Michael De Vlieger, Oct 24 2018 *)

Prog

(PARI) a(n) = {my(d=digits(n), v = vector(10), res = 0, t = 0); for(i=1, #d, v[d[i]+1]++); for(i=1, #d, if(v[d[i]+1]==1, t = 1; res=10 * res + d[i])); res - !t + !n} \\ David A. Corneth, Oct 24 2018
(Python)
def A320485(n):
    return (lambda x: int(x) if x != '' else -1)(''.join(d if str(n).count(d) == 1 else '' for d in str(n))) # Chai Wah Wu, Nov 19 2018

Crossrefs

See A320486 for another version.

Cf. A010784, A115853, A321008-A321012.

Sequence in context: A118541 A084905 A180409 * A321802 A337864 A106612

Adjacent sequences: A320482 A320483 A320484 * A320486 A320487 A320488

Keyword

sign,base,look

Author

N. J. A. Sloane, Oct 24 2018

Status

approved