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

Author

Eric Angelini, Oct 18 2023

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

a(n) = if(n > 0, (n%9 + 1)*(10^(n\9 + 2)-1)/9 - 10) \\ Andrew Howroyd, Oct 22 2023

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