A033075 -id:A033075 - cp's OEIS frontend

A352927 Numbers whose digits are nonzero, consecutive, and all increasing or all decreasing.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 123, 234, 321, 345, 432, 456, 543, 567, 654, 678, 765, 789, 876, 987, 1234, 2345, 3456, 4321, 4567, 5432, 5678, 6543, 6789, 7654, 8765, 9876, 12345, 23456, 34567, 45678, 54321, 56789, 65432, 76543, 87654, 98765, 123456, 234567, 345678

Offset: 1

N. J. A. Sloane, May 01 2022, following a suggestion from Ralph Sieber

There are 81 terms, corresponding to numbers that start with i and end with j, for 1 <= i <= 9, 1 <= j <= 9. - Michael S. Branicky, May 01 2022

Michael S. Branicky, Table of n, a(n) for n = 1..81

Cf. A033075, A082927, A138141, A215014.

Join[Range[9],Select[Range[350000],DigitCount[#,10,0]==0&&(Union[Differences[IntegerDigits[ #]]]=={1}||Union[Differences[IntegerDigits[#]]]=={-1})&]] (* Harvey P. Dale, Aug 13 2023 *)

def sgn(n): return 1 if n >= 0 else -1
def afull(): return sorted(int("".join(map(str, range(i, j+sgn(j-i), sgn(j-i))))) for i in range(1, 10) for j in range(1, 10))
print(afull()) # Michael S. Branicky, May 01 2022

A252481 Numbers whose set of digits is simply connected to 1.

Original entry on oeis.org

1, 10, 11, 12, 21, 100, 101, 102, 110, 111, 112, 120, 121, 122, 123, 132, 201, 210, 211, 212, 213, 221, 231, 312, 321, 1000, 1001, 1002, 1010, 1011, 1012, 1020, 1021, 1022, 1023, 1032, 1100, 1101, 1102, 1110, 1111, 1112, 1120, 1121, 1122, 1123, 1132, 1200, 1201, 1202, 1203, 1210, 1211, 1212, 1213, 1220, 1221, 1222, 1223

Offset: 1

M. F. Hasler, Dec 24 2014

"Simply connected" means that there must not be a "hole" in the set of digits. E.g., {1,2,4} would not be allowed since '3' is missing.

Cf. A032981, A050278, A033075, A010785, A108965, A134336, A252490.

is(n)={d=Set(digits(n));d[1]==1 || (#d>1&&d[2]==1) || return; d[#d]==#d-!d[1]}

def ok(n):
  s = set(str(n)); return '1' in s and len(s) == ord(max(s))-ord(min(s))+1
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
print(aupto(1223)) # Michael S. Branicky, Jan 10 2021

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

Original entry on oeis.org

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

Ofer Zivony, Sep 14 2022

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.

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

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

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

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

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)

cp's OEIS Frontend

A352927 Numbers whose digits are nonzero, consecutive, and all increasing or all decreasing.

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A252481 Numbers whose set of digits is simply connected to 1.

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

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Maple

Mathematica

PARI

Python