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A376425
Numbers whose adjacent digits differ by at most 1 modulo 10.
2
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
1,3
COMMENTS
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.
FORMULA
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)
EXAMPLE
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.
MAPLE
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
PROG
(PARI) 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}
CROSSREFS
Subsequence of A252490 union {0}.
Sequence in context: A257737 A130577 A252490 * A178403 A134336 A131207
KEYWORD
nonn,base
AUTHOR
Andrew Howroyd, Sep 22 2024
STATUS
approved