A357142 Nonnegative numbers all of whose pairs of consecutive decimal digits are adjacent digits, where 9 and 0 are considered adjacent.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 90, 98, 101, 109, 121, 123, 210, 212, 232, 234, 321, 323, 343, 345, 432, 434, 454, 456, 543, 545, 565, 567, 654, 656, 676, 678, 765, 767, 787, 789, 876, 878, 890, 898, 901, 909

Offset: 1

Author

Ofer Zivony, Sep 14 2022

Keywords

• nonn
• base
• easy

Comments

This is very similar to A033075, with the exception of considering 0 and 9 as adjacent digits. This allows these digits to be equal to the other digits, making it a more balanced list.

Crossrefs

Cf. A032981, A033075, A043089 (ternary analog), A048491.

Programs

Maple

q:= n-> (l-> andmap(x-> x in {1, 9}, {seq(abs(l[i]-l[i-1]),
             i=2..nops(l))}))(convert(n, base, 10)):
select(q, [$0..1000])[];  # Alois P. Heinz, Sep 14 2022

Mathematica

q[n_] := AllTrue[Abs @ Differences @ IntegerDigits[n], MemberQ[{1, 9}, #] &]; Select[Range[0, 1000], q] (* Amiram Eldar, Sep 15 2022 *)

PARI

a(n) = { n--; for (b=0, oo, if (n <= 9*2^b, my (v=ceil(n/2^b), p=(n-1)%(2^b)); while (b>0, v=10*v+vecsort([(v-1)%10, (v+1)%10])[1+bittest(p,b--)];); return (v), n -= 9*2^b)) } \\ Rémy Sigrist, Sep 15 2022

Python

def add_dig(x):
  d = (x%10-1)%8 if x%10 != 0 else 1
  return 10*x+d
def try_incr(x):
  if x < 10: return x+1
  r = x//10
  d2 = r%10
  d = max((d2+1)%10,(d2-1)%10)
  return 10*r+d
def incr(x):
  new_x=try_incr(x)
  return new_x if new_x>x else add_dig(incr(x//10))
x = 0
for n in range(1,1000):
  print(f"{n} {x}")
  x = incr(x)