A318700 -id:A318700 - cp's OEIS frontend

A309539 Positive numbers that contain both odd and even digits, with no digit repeated.

10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 102, 103, 104, 105, 106, 107, 108, 109, 120, 123, 124, 125, 126, 127, 128, 129, 130, 132, 134, 136

Offset: 1

Enrique Navarrete, Aug 06 2019

Unlike A318700, where digits can be repeated, this sequence is finite; last term is 9876543210.

			49 and 50 are in the sequence but 19 and 20 are not.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A318700, A010784.

filter:= proc(n) local L;
  L:= convert(n,base,10);
  nops(L) = nops(convert(L,set)) and convert(L mod 2,set) = {0,1};
end proc:
select(filter, [$10 .. 1000]); # Robert Israel, Jan 09 2025

boeQ[n_]:=Max[DigitCount[n]]==1&&IntegerLength[n]>Count[ IntegerDigits[ n],?EvenQ]>0; Select[Range[150],boeQ] (* _Harvey P. Dale, Jul 02 2020 *)

isok(n) = my(d=digits(n)); (#d == #Set(d)) && #select(x->(x%2), d) && #select(x->!(x%2), d); \\ Michel Marcus, Aug 07 2019

A309390 Set a(1)=10. Thereafter a(n) is the smallest positive number not yet in the sequence that contains exactly one even digit and one odd digit from a(n-1).

Original entry on oeis.org

10, 100, 101, 102, 12, 21, 112, 120, 103, 30, 130, 104, 14, 41, 114, 124, 121, 122, 123, 23, 32, 132, 125, 25, 52, 152, 126, 16, 61, 106, 105, 50, 150, 107, 70, 170, 108, 18, 81, 118, 128, 127, 27, 72, 172, 129, 29, 92, 192, 142, 134, 34, 43, 143, 140, 109, 90, 190, 110, 160, 116

Offset: 1

Enrique Navarrete, Jul 27 2019

Numbers such as 3, 8, 20, 31, and 42 are not in the sequence since by definition all terms must contain both odd and even digits.

			a(2)=100 since it is the smallest number not yet in the sequence that contains an even digit (0) and an odd digit (1) from a(1)=10.
a(7)=112 since it is the smallest number not yet in the sequence that contains an even digit (2) and an odd digit (1) from a(6)=21.
a(27)=126 is not 105 since 105 would contain two odd digits (1 and 5) from a(26)=152.

Cf. A318700 (positive numbers that contain both odd and even digits).

A309540 a(n) is the smallest positive number not yet in the sequence that contains exactly one even digit and exactly one odd digit from a(n-1), and no digit in a(n) is repeated.

Original entry on oeis.org

10, 102, 12, 21, 120, 103, 30, 130, 104, 14, 41, 124, 123, 23, 32, 132, 125, 25, 52, 152, 126, 16, 61, 106, 105, 50, 150, 107, 70, 170, 108, 18, 81, 128, 127, 27, 72, 172, 129, 29, 92, 192, 142, 134, 34, 43, 143, 140, 109, 90, 190, 160, 136, 36, 63, 163

Offset: 1

Enrique Navarrete, Aug 06 2019

			a(2)=102: a(2) is not 100 (since zero would be repeated), nor 101 (since 1 would be repeated).

Robert Israel, Table of n, a(n) for n = 1..40534

Cf. A184992, A318700, A309390, A309539, A076654.

filter:= proc(n) local L;
  L:= convert(n,base,10);
  nops(L) = nops(convert(L,set)) and convert(L mod 2,set) = {0,1};
end proc:
Cands:= select(filter, [$11 .. 1000]): nC:= nops(Cands):
R:= 10: r:= 10: r0, r1:= selectremove(type, convert(convert(r,base,10),set),even):
for count from 1 do
  found:= false;
  for i from 1 to nC+1-count do
    x:= Cands[i];
    Lx:= convert(convert(x,base,10),set);
    if nops(Lx intersect r0) = 1 and nops(Lx intersect r1) = 1 then
      found:= true;
      R:= R, x;
      r:= x;
      Cands:= subsop(i=NULL, Cands);
      r0, r1:= selectremove(type, convert(convert(r,base,10),set),even);
      break
    fi
  od;
  if not found then break fi;
od:
R; # Robert Israel, Jan 09 2025

Edited by Robert Israel, Jan 10 2025

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A309539 Positive numbers that contain both odd and even digits, with no digit repeated.

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A309390 Set a(1)=10. Thereafter a(n) is the smallest positive number not yet in the sequence that contains exactly one even digit and one odd digit from a(n-1).

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A309540 a(n) is the smallest positive number not yet in the sequence that contains exactly one even digit and exactly one odd digit from a(n-1), and no digit in a(n) is repeated.

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