A180204 Base-10 representation of numbers k which, in base 2, satisfy abs(k + reverse(k) - reverse(k + reverse(k))) = k.

0, 1, 3, 5, 7, 9, 15, 17, 21, 27, 31, 33, 45, 51, 63, 65, 73, 85, 90, 93, 99, 107, 119, 127, 129, 153, 165, 186, 189, 195, 219, 231, 255, 257, 273, 297, 313, 325, 341, 365, 378, 381, 387, 403, 427, 443, 455, 471, 495, 511, 513, 561, 585, 633, 645, 678, 693, 717

Offset

1,3

Comments

A006995 is a subsequence of this sequence, because a palindrome plus its reverse is equivalent to itself times 2, which in base 2 is equivalent to appending a zero to the number. This zero is eliminated by the second reversal, leaving the reverse of the original number, which, since it is a palindrome, is the equivalent of the number itself, and 2x - x = x.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

rev2:= proc(n) local L, i;
  L:= convert(n, base, 2);
  add(L[-i]*2^(i-1), i=1..nops(L))
end proc:
filter:= k -> abs(k + rev2(k) - rev2(k + rev2(k))) = k:
select(filter, [$0..1000]); # Robert Israel, Dec 24 2025

Mathematica

rev[x_, b_] := FromDigits[Reverse[IntegerDigits[x, b]], b]; revadd[x_, b_] := rev[x, b] + x; revsub[x_, b_] := Abs[x - rev[x, b]]; s = {}; Do [If[revsub[revadd[ x, 2], 2] == x, AppendTo[s, x]], {x, START, FINISH}]; s

Crossrefs

Cf. A179697.

Sequence in context: A374199 A359402 A329358 * A006995 A163410 A329419

Adjacent sequences: A180201 A180202 A180203 * A180205 A180206 A180207

Keyword

base,nonn

Author

Dylan Hamilton, Aug 15 2010

Extensions

Offset corrected by Robert Israel, Dec 24 2025

Status

approved