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

%I A363823 #24 Oct 22 2023 15:13:54
%S A363823 13,24,35,46,57,68,79,202,313,424,535,646,757,868,979,1091,2202,3313,
%T A363823 4424,5535,6646,7757,8868,9979,11091,22202,33313,44424,55535,66646,
%U A363823 77757,88868,99979,111091,222202,333313,444424,555535,666646,777757,888868,999979
%N A363823 Moving the rightmost digit of a number to place it furthest to the left adds 18 to the number.
%C A363823 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
%H A363823 Andrew Howroyd, <a href="/A363823/b363823.txt">Table of n, a(n) for n = 1..1000</a>
%e A363823 a(1) = 13 plus 18 = 31; the rightmost 3 is now in front and 1 at the end;
%e A363823 a(2) = 24 plus 18 = 42; the rightmost 4 is now in front and 2 at the end;
%e A363823 a(3) = 35 plus 18 = 53; the rightmost 5 is now in front and 3 at the end;
%e A363823 a(4) = 46 plus 18 = 64; the rightmost 6 is now in front and 4 at the end;
%e A363823 ...
%e A363823 a(8) = 202 plus 18 = 220; the rightmost 2 is now in front and 0 at the end; etc.
%t A363823 Select[Range[10^6], FromDigits[RotateRight[IntegerDigits[#]]]-#==18 &] (* _Stefano Spezia_, Oct 19 2023 *)
%o A363823 (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
%o A363823 (Python)
%o A363823 def ok(n): s = str(n); return int(s[-1]+s[:-1]) - n == 18
%o A363823 print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Oct 19 2023
%Y A363823 Cf. A010785 (repdigit numbers), A363820.
%K A363823 base,nonn
%O A363823 1,1
%A A363823 _Eric Angelini_, Oct 18 2023