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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. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
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.
LINKS
MAPLE
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
MATHEMATICA
q[n_] := AllTrue[Abs @ Differences @ IntegerDigits[n], MemberQ[{1, 9}, #] &]; Select[Range[0, 1000], q] (* Amiram Eldar, Sep 15 2022 *)
PROG
(Python)
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)
(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
CROSSREFS
Cf. A032981, A033075, A043089 (ternary analog), A048491.
Sequence in context: A328273 A342262 A255734 * A033075 A215014 A292439
KEYWORD
nonn,base,easy
AUTHOR
Ofer Zivony, Sep 14 2022
STATUS
approved

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Last modified June 23 06:39 EDT 2024. Contains 373629 sequences. (Running on oeis4.)