A252490 -id:A252490 - cp's OEIS frontend

A376425 Numbers whose adjacent digits differ by at most 1 modulo 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 90, 98, 99, 100, 101, 109, 110, 111, 112, 121, 122, 123, 210, 211, 212, 221, 222, 223, 232, 233, 234, 321, 322, 323, 332, 333, 334, 343, 344, 345, 432

Offset: 1

Andrew Howroyd, Sep 22 2024

Neighbors of 9 are 0 and 8.

Except for the initial zero this is a strict subsequence of A252490 which uses the same neighborhood rule for digits but considers an unordered set of digits. The first difference is that 102 is included by A252490 but excluded here.

			11 is a term because 1 = 1.
32 is a terms because 3 is a neighbor of 2.
109 is a term because 1 is a neighbor of 0 and 0 is a neighbor of 9 (modulo 10).
121 is a term because 1 is a neighbor of 2 and 2 is a neighbor of 1.

Subsequence of A252490 union {0}.

Cf. A068148, A068149, A087553.

f:= proc(n) local i;
   seq(10*n+i,i= sort([n-1,n,n+1] mod 10))
end proc:
S:= [$1..9]: R:= 0,op(S):
for i from 1 to 3 do
  S:= map(f,S); R:= R,op(S)
od:
R; # Robert Israel, Sep 22 2024

isok(k)={my(v=digits(k)); for(i=2, #v, my(t=abs(v[i]-v[i-1])); if(t>1&&t<9, return(0))); 1}

From Robert Israel, Sep 22 2024 (Start):
Let a(n) mod 10 = d.
If 1 <= d <= 8 then a(3 n + 6 + j) = 10 a(n) + d + j for j = -1, 0, 1.
If d = 0 and n > 1, then a(3 n + 5) = 10 a(n), a(3 n + 6) = 10 a(n) + 1, a(3 n + 7) = 10 a(n) + 9.
If d = 9, then a(3 n + 5) = 10 a(n), a(3 n + 6) = 10 a(n) + 8, a(3 n + 7) = 10 a(n) + 9.
(End)

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

cp's OEIS Frontend

A376425 Numbers whose adjacent digits differ by at most 1 modulo 10.

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