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

1,1

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A010785 (repdigit numbers), A363820.

Sequence in context: A104342 A119590 A266912 * A032607 A335973 A190040

Adjacent sequences: A363820 A363821 A363822 * A363824 A363825 A363826

Keyword

base,nonn

Author

Eric Angelini, Oct 18 2023

Status

approved