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.

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

1,1

Links

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

Example

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

Maple

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

Crossrefs

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

Sequence in context: A061107 A015498 A266283 * A039393 A199168 A297062

Adjacent sequences: A309537 A309538 A309539 * A309541 A309542 A309543

Keyword

nonn,base,fini,full,look

Author

Enrique Navarrete, Aug 06 2019

Extensions

Edited by Robert Israel, Jan 10 2025

Status

approved