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
Examples
a(2)=102: a(2) is not 100 (since zero would be repeated), nor 101 (since 1 would be repeated).
Links
- Robert Israel, Table of n, a(n) for n = 1..40534
Programs
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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
Extensions
Edited by Robert Israel, Jan 10 2025