A363820 Moving the rightmost digit of a number to place it furthest to the left adds 9 to the number.

12, 23, 34, 45, 56, 67, 78, 89, 101, 212, 323, 434, 545, 656, 767, 878, 989, 1101, 2212, 3323, 4434, 5545, 6656, 7767, 8878, 9989, 11101, 22212, 33323, 44434, 55545, 66656, 77767, 88878, 99989, 111101, 222212, 333323, 444434, 555545, 666656, 777767, 888878, 999989

Offset

1,1

Comments

All terms k are repdigit numbers minus 10. The sequence starts with 22 - 10 = 12. - Andrew Howroyd, Oct 22 2023

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Example

a(1) = 12 plus 9 = 21; the rightmost 2 is now in front and 1 at the end;
a(2) = 23 plus 9 = 32; the rightmost 3 is now in front and 2 at the end;
a(3) = 34 plus 9 = 43; the rightmost 4 is now in front and 3 at the end;
a(4) = 45 plus 9 = 54; the rightmost 5 is now in front and 4 at the end;
...
a(9) = 101 plus 9 = 110; the rightmost 1 is now in front and 0 at the end; etc.

Mathematica

Select[Range[10^6], FromDigits[RotateRight[IntegerDigits[#]]]-#==9 &] (* Stefano Spezia, Oct 18 2023 *)

Prog

(Python)
def ok(n): s = str(n); return int(s[-1]+s[:-1]) - n == 9
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 18 2023
(PARI) a(n) = if(n > 0, (n%9 + 1)*(10^(n\9 + 2)-1)/9 - 10) \\ Andrew Howroyd, Oct 22 2023

Crossrefs

Cf. A010785 (repdigit numbers), A228157, A363823.

Sequence in context: A004960 A098953 A228157 * A072485 A035333 A001704

Adjacent sequences: A363817 A363818 A363819 * A363821 A363822 A363823

Keyword

base,nonn

Author

Eric Angelini, Oct 18 2023

Status

approved