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

1,2

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.

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

Prog

(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! */

Crossrefs

Cf. A249591, A067581.

Sequence in context: A172503 A107859 A294069 * A067524 A069555 A069035

Adjacent sequences: A249582 A249583 A249584 * A249586 A249587 A249588

Keyword

nonn,base

Author

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

Status

approved