A363823 Moving the rightmost digit of a number to place it furthest to the left adds 18 to the number.

13, 24, 35, 46, 57, 68, 79, 202, 313, 424, 535, 646, 757, 868, 979, 1091, 2202, 3313, 4424, 5535, 6646, 7757, 8868, 9979, 11091, 22202, 33313, 44424, 55535, 66646, 77757, 88868, 99979, 111091, 222202, 333313, 444424, 555535, 666646, 777757, 888868, 999979

Offset: 1

Author

Eric Angelini, Oct 18 2023

Keywords

• base
• nonn

Comments

All terms k are repdigit numbers minus 20. In addition, k is required to have the same number of digits as k + 18. This excludes 22-20 = 2 and 111-20 = 91. - Andrew Howroyd, Oct 22 2023

Examples

			a(1) = 13 plus 18 = 31; the rightmost 3 is now in front and 1 at the end;
a(2) = 24 plus 18 = 42; the rightmost 4 is now in front and 2 at the end;
a(3) = 35 plus 18 = 53; the rightmost 5 is now in front and 3 at the end;
a(4) = 46 plus 18 = 64; the rightmost 6 is now in front and 4 at the end;
...
a(8) = 202 plus 18 = 220; the rightmost 2 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), A363820.

Programs

Mathematica

Select[Range[10^6], FromDigits[RotateRight[IntegerDigits[#]]]-#==18 &] (* Stefano Spezia, Oct 19 2023 *)

PARI

a(n) = if(n > 0, n++; n+=(n>=9); (n%9 + 1)*(10^(n\9 + 2)-1)/9 - 20) \\ Andrew Howroyd, Oct 18 2023

Python

def ok(n): s = str(n); return int(s[-1]+s[:-1]) - n == 18
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Oct 19 2023