

A180204


Base10 representation of numbers k which, in base 2, satisfy abs(k + reverse(k)  reverse(k + reverse(k))) = k.


1



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
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OFFSET

0,3


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

Table of n, a(n) for n=0..57.


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: A305409 A342572 A329358 * A006995 A163410 A329419
Adjacent sequences: A180201 A180202 A180203 * A180205 A180206 A180207


KEYWORD

base,nonn


AUTHOR

Dylan Hamilton, Aug 15 2010


STATUS

approved



