cp's OEIS Frontend

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

%I A357142 #36 Dec 09 2022 23:04:32
%S A357142 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,
%T A357142 90,98,101,109,121,123,210,212,232,234,321,323,343,345,432,434,454,
%U A357142 456,543,545,565,567,654,656,676,678,765,767,787,789,876,878,890,898,901,909
%N A357142 Nonnegative numbers all of whose pairs of consecutive decimal digits are adjacent digits, where 9 and 0 are considered adjacent.
%C A357142 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.
%p A357142 q:= n-> (l-> andmap(x-> x in {1, 9}, {seq(abs(l[i]-l[i-1]),
%p A357142              i=2..nops(l))}))(convert(n, base, 10)):
%p A357142 select(q, [$0..1000])[];  # _Alois P. Heinz_, Sep 14 2022
%t A357142 q[n_] := AllTrue[Abs @ Differences @ IntegerDigits[n], MemberQ[{1, 9}, #] &]; Select[Range[0, 1000], q] (* _Amiram Eldar_, Sep 15 2022 *)
%o A357142 (Python)
%o A357142 def add_dig(x):
%o A357142   d = (x%10-1)%8 if x%10 != 0 else 1
%o A357142   return 10*x+d
%o A357142 def try_incr(x):
%o A357142   if x < 10: return x+1
%o A357142   r = x//10
%o A357142   d2 = r%10
%o A357142   d = max((d2+1)%10,(d2-1)%10)
%o A357142   return 10*r+d
%o A357142 def incr(x):
%o A357142   new_x=try_incr(x)
%o A357142   return new_x if new_x>x else add_dig(incr(x//10))
%o A357142 x = 0
%o A357142 for n in range(1,1000):
%o A357142   print(f"{n} {x}")
%o A357142   x = incr(x)
%o A357142 (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
%Y A357142 Cf. A032981, A033075, A043089 (ternary analog), A048491.
%K A357142 nonn,base,easy
%O A357142 1,3
%A A357142 _Ofer Zivony_, Sep 14 2022