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

1,3

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.

Links

Table of n, a(n) for n=1..62.

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 *)

Prog

(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)
(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

Crossrefs

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

Sequence in context: A328273 A342262 A255734 * A033075 A215014 A292439

Adjacent sequences: A357139 A357140 A357141 * A357143 A357144 A357145

Keyword

nonn,base,easy

Author

Ofer Zivony, Sep 14 2022

Status

approved