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A175298 Smallest number >=n whose binary representation is palindromic and has a 1 whenever the binary representation of n has a 1. 76
0, 1, 3, 3, 5, 5, 7, 7, 9, 9, 15, 15, 15, 15, 15, 15, 17, 17, 27, 27, 21, 21, 31, 31, 27, 27, 27, 27, 31, 31, 31, 31, 33, 33, 51, 51, 45, 45, 63, 63, 45, 45, 63, 63, 45, 45, 63, 63, 51, 51, 51, 51, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 65, 65, 99, 99, 85, 85, 119, 119, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Old name: "Convert n to binary. OR each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result."

By "respective" digits of binary n and binary A030101(n), the rightmost digit of A030101(n) ( which is a 1) is OR'ed with the rightmost digit of n. A030101(n) is represented with the appropriate number of leading 0's.

This is the binary next-palindrome function, the base-2 analog of A262038. - N. J. A. Sloane, Dec 08 2015

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..16383

EXAMPLE

20 in binary is 10100. The reversal of the binary digits is 00101. So, from leftmost to rightmost respective digits, we OR 10100 and 00101: 1 OR 0 = 1. 0 OR 0 = 0. 1 OR 1 = 1. 0 OR 0 = 0. And 0 OR 1 = 1. So, 10100 OR 00101 is 10101, which is 21 in decimal. So a(20) = 21.

MATHEMATICA

Table[f = IntegerDigits[x, 2]; f = f + Reverse[f]; FromDigits[ Table[If[Positive[f[[r]]], 1, 0], {r, 1, Length[f]}], 2], {x, STARTPOINT, ENDPOINT}] (* Dylan Hamilton, Oct 15 2010 *)

f[n_] := Block[{id = IntegerDigits[n, 2]}, FromDigits[ BitOr[ id, Reverse@id], 2]]; Array[f, 72] (* Robert G. Wilson v, Nov 07 2010 *)

CROSSREFS

Cf. A006995, A030101, A175297, A262038.

Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.

Sequence in context: A237718 A245149 A206914 * A245148 A073737 A237716

Adjacent sequences:  A175295 A175296 A175297 * A175299 A175300 A175301

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Mar 24 2010

EXTENSIONS

Extended, with redundant initial entries included, by Dylan Hamilton, Oct 15 2010

Edited with new name and offset by N. J. A. Sloane, Dec 08 2015

STATUS

approved

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Last modified August 20 06:39 EDT 2019. Contains 326139 sequences. (Running on oeis4.)