A363823 - OEIS

%I #24 Oct 22 2023 15:13:54

%S 13,24,35,46,57,68,79,202,313,424,535,646,757,868,979,1091,2202,3313,

%T 4424,5535,6646,7757,8868,9979,11091,22202,33313,44424,55535,66646,

%U 77757,88868,99979,111091,222202,333313,444424,555535,666646,777757,888868,999979

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

%C 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 Andrew Howroyd, <a href="/A363823/b363823.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 13 plus 18 = 31; the rightmost 3 is now in front and 1 at the end;

%e a(2) = 24 plus 18 = 42; the rightmost 4 is now in front and 2 at the end;

%e a(3) = 35 plus 18 = 53; the rightmost 5 is now in front and 3 at the end;

%e a(4) = 46 plus 18 = 64; the rightmost 6 is now in front and 4 at the end;

%e ...

%e a(8) = 202 plus 18 = 220; the rightmost 2 is now in front and 0 at the end; etc.

%t Select[Range[10^6], FromDigits[RotateRight[IntegerDigits[#]]]-#==18 &] (* _Stefano Spezia_, Oct 19 2023 *)

%o (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 (Python)

%o def ok(n): s = str(n); return int(s[-1]+s[:-1]) - n == 18

%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Oct 19 2023

%Y Cf. A010785 (repdigit numbers), A363820.

%K base,nonn

%O 1,1

%A _Eric Angelini_, Oct 18 2023