OFFSET
1,1
COMMENTS
I do not know of any numbers that satisfy abs(k + reverse(k) - reverse(k + reverse(k))) = abs(k - reverse(k)) + reverse(abs(k - reverse(k))) without satisfying abs(k + reverse(k) - reverse(k + reverse(k))) = abs(k - reverse(k)) + reverse(abs(k - reverse(k))) = k. All terms appear to have 2^1 and 3^something in their factorizations. All numbers whose binary representation is of the form 10(j 1s)010, where j>1, appear to be terms of this sequence.
EXAMPLE
k = 90 is a term:
k = 1011010_2;
reverse(k) = 101101_2;
k + reverse(k) = 1011010_2 + 101101_2 = 10000111_2;
reverse(k + reverse(k)) = 11100001_2;
k - reverse(k) = 1011010_2 - 101101_2 = 101101_2;
reverse(k - reverse(k)) = 101101_2;
abs(k + reverse(k) - reverse(k + reverse(k))) = abs(10000111_2 - 101101_2) = 1011010_2 = k;
abs(k - reverse(k)) + reverse(abs(k - reverse(k))) = abs(101101_2) + reverse(abs(101101_2)) = 101101_2 + 101101_2 = 1011010_2 = k.
MATHEMATICA
(* Checks all values between "START" and "FINISH" *) rev[x_, b_] := FromDigits[Reverse[IntegerDigits[x, b]], b]; revadd[x_, b_] := rev[x, b] + x ; revsub[x_, b_] := Abs[x - rev[x, b]]; t = {}; Do [If[revsub[revadd[ x, 2], 2] == revadd[revsub[x, 2], 2] == x, AppendTo[t, x]], {x, START, FINISH}]; t
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Dylan Hamilton, Jul 24 2010
EXTENSIONS
More terms and a more efficient program from Dylan Hamilton, Aug 15 2010
Edited by Jon E. Schoenfield, Jan 04 2022
STATUS
approved