A036839 RATS(n): Reverse Add Then Sort the digits.

0, 2, 4, 6, 8, 1, 12, 14, 16, 18, 11, 22, 33, 44, 55, 66, 77, 88, 99, 11, 22, 33, 44, 55, 66, 77, 88, 99, 11, 112, 33, 44, 55, 66, 77, 88, 99, 11, 112, 123, 44, 55, 66, 77, 88, 99, 11, 112, 123, 134, 55, 66, 77, 88, 99, 11, 112, 123, 134, 145, 66, 77

Offset

0,2

Comments

a(n) = RATS(n), not RATS(a(n-1)).

Row 10 of A288535. - Andrey Zabolotskiy, Jun 14 2017

Links

Indranil Ghosh, Table of n, a(n) for n = 0..50000 (terms 0..1000 from T. D. Noe)

R. K. Guy, Conway's RATS and other reversals, Unsolved Problems Column, American Math. Monthly, Vol. 96, pp. 425-428, May 1989.

Eric Weisstein's World of Mathematics, RATS Sequence

Formula

Form m by Reversing the digits of n, Add m to n Then Sort the digits of the sum into increasing order to get a(n).

a(n) = A004185(A056964(n)). [Reinhard Zumkeller, Mar 14 2012]

Example

1 -> 1 + 1 = 2, so a(1) = 2; 3 -> 3 + 3 = 6, so a(3) = 6.

Maple

read transforms; RATS := n -> digsort(n + digrev(n));

Mathematica

FromDigits[Sort[IntegerDigits[#+FromDigits[Reverse [IntegerDigits[#]]]]]] & /@Range[0, 80]  (* Harvey P. Dale, Mar 26 2011 *)

Prog

(Haskell)
a036839 = a004185 . a056964  -- Reinhard Zumkeller, Mar 14 2012
(Python)
def A036839(n):
    x = str(n+int(str(n)[::-1]))
    return int("".join(sorted(x))) # Indranil Ghosh, Jan 28 2017

Crossrefs

Cf. A004000, A004185, A288535.

Cf. A161593, A114611, A009994, A004086.

Sequence in context: A007396 A169910 A004519 * A004093 A106202 A351330

Adjacent sequences: A036836 A036837 A036838 * A036840 A036841 A036842

Keyword

nonn,base,nice,easy,look

Author

N. J. A. Sloane, Jan 19 2002

Status

approved