A249585 Lexicographically earliest permutation of the positive integers such that a(n+1) has at least one digit which increased by 1 is a digit of a(n).

1, 10, 20, 11, 30, 2, 12, 13, 21, 14, 3, 22, 15, 4, 23, 16, 5, 24, 17, 6, 25, 18, 7, 26, 19, 8, 27, 31, 28, 37, 29, 38, 32, 41, 33, 42, 34, 35, 40, 36, 45, 39, 48, 43, 52, 44, 53, 46, 50, 47, 56, 49, 58, 54, 63, 51, 60, 55, 64, 57, 61, 59, 68, 65, 74, 62, 71, 66, 75, 67, 69, 78, 70, 76, 85, 72, 81, 73, 82, 77, 86, 79, 80, 87, 96, 83, 92, 84, 93, 88

Offset: 1

Author

Eric Angelini and M. F. Hasler, Nov 01 2014

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• E. Angelini, Downgrade one of the digits of a(n-1), Nov 01 2014.

Crossrefs

Cf. A249591, A067581.

Programs

Maple

N:= 200: # to get the first N terms
  S:= {}:
  m:= 2:
a[1]:= 1:
xnext:= proc(x)
    local j, Sc;
    Sc:= select(`>`,S,x);
    if Sc <> {} then min(Sc)
    elif x < m then m
    else x+1
    fi
end proc:
for n from 2 to N do
  adigs:= convert(convert(a[n-1],base,10),set);
  bdigs:= {$0..8} intersect map(`-`,adigs,1);
  c:= 0;
  do
    c:= xnext(c);
    if convert(convert(c,base,10),set) intersect bdigs <> {} then
       if member(c,S) then S:= S minus {c}
       else
         S:= S union {$m .. c-1};
         m:= c + 1;
       fi;
       a[n]:= c;
       break
    fi
  od;
od:
seq(a[n],n=1..N); # Robert Israel, Nov 03 2014

PARI

A249585(n,show=0,a=1,u=[])={for(i=2,n, show&&print1(a","); u=setunion(u,Set(a)); D=Set(apply(d->d-1,digits(a))); while(setsearch(u,1+m=vecmin(u)),u=setminus(u,Set(m))); for(m=m+1,9e9,!setsearch(u,m)&&#setintersect(D,Set(digits(m))) &&(a=m)&&break));a} /* Using a more natural and simpler until() loop is 10x slower! */