A179697 Base-10 representation of numbers k which, in base 2, satisfy abs(k + reverse(k) - reverse(k + reverse(k))) = abs(k - reverse(k)) + reverse(abs(k - reverse(k))) = k.

90, 186, 378, 762, 1530, 3066, 6138, 12282, 23130, 24570, 46170, 49146, 92250, 95418, 98298, 184410, 190650, 196602, 368730, 381114, 387450, 393210, 737370, 762042, 774522, 786426, 1474650, 1523898, 1548666, 1561338, 1572858, 2949210, 3047610, 3096954, 3121914, 3145722, 5898330, 5921370, 6095034, 6193530, 6243066, 6268410, 6291450

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.

Links

Table of n, a(n) for n=1..43.

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

Cf. A030101 (reverse base 2).

Sequence in context: A255785 A366740 A119896 * A211442 A282473 A044422

Adjacent sequences: A179694 A179695 A179696 * A179698 A179699 A179700

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