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Numbers whose adjacent digits differ by at most 1 modulo 10.
2

%I #10 Sep 22 2024 15:20:24

%S 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,

%T 66,67,76,77,78,87,88,89,90,98,99,100,101,109,110,111,112,121,122,123,

%U 210,211,212,221,222,223,232,233,234,321,322,323,332,333,334,343,344,345,432

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

%C Neighbors of 9 are 0 and 8.

%C 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.

%F From _Robert Israel_, Sep 22 2024 (Start):

%F Let a(n) mod 10 = d.

%F If 1 <= d <= 8 then a(3 n + 6 + j) = 10 a(n) + d + j for j = -1, 0, 1.

%F 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.

%F 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.

%F (End)

%e 11 is a term because 1 = 1.

%e 32 is a terms because 3 is a neighbor of 2.

%e 109 is a term because 1 is a neighbor of 0 and 0 is a neighbor of 9 (modulo 10).

%e 121 is a term because 1 is a neighbor of 2 and 2 is a neighbor of 1.

%p f:= proc(n) local i;

%p seq(10*n+i,i= sort([n-1,n,n+1] mod 10))

%p end proc:

%p S:= [$1..9]: R:= 0,op(S):

%p for i from 1 to 3 do

%p S:= map(f,S); R:= R,op(S)

%p od:

%p R; # _Robert Israel_, Sep 22 2024

%o (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}

%Y Subsequence of A252490 union {0}.

%Y Cf. A068148, A068149, A087553.

%K nonn,base

%O 1,3

%A _Andrew Howroyd_, Sep 22 2024