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

Author

N. J. A. Sloane, Oct 24 2018

Keywords

• sign
• base
• look

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

Examples

			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.
		

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)

Crossrefs

See A320486 for another version.

Cf. A010784, A115853, A321008-A321012.

Programs

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 *)

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

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