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A145800 a(n) = the smallest positive integer that is an (odd) palindrome when represented in binary and that contains within it the binary representation of n. 5
1, 5, 3, 9, 5, 27, 7, 17, 9, 21, 27, 51, 27, 93, 15, 33, 17, 73, 51, 165, 21, 45, 93, 99, 51, 107, 27, 231, 93, 189, 31, 65, 33, 273, 99, 73, 165, 153, 231, 325, 165, 85, 107, 717, 45, 93, 189, 195, 99, 403, 51, 843, 107, 219, 119, 455, 231, 471, 119, 633, 189, 381, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For n is a power of 2 (A000079), a(n) = 2*n + 1.
This sequence contains, by definition, those binary palindromes that are odd, i.e., those palindromes without leading zeros. In other words, only integers occurring in sequence A006995 occur in this sequence.
a(A006995(n)) = A006995(n). - Ray Chandler, Oct 26 2008
LINKS
EXAMPLE
6 in binary is 110. Those integers which contain 110 in their binary representations are 6 (110 in binary), 12 (1100 in binary), 13 (1101 in binary), 14 (1110 in binary), 22 (10110 in binary), 24 (11000 in binary), 25 (11001 in binary), 26 (11010 in binary), 27 (11011 in binary), etc... Now, 27 (11011 in binary) is the smallest of these integers that is a binary palindrome; so a(6) = 27.
MATHEMATICA
Table[With[{d = IntegerDigits[n, 2]}, k = 1; While[Nand[SequenceCount[Set[m, IntegerDigits[k, 2]], d] > 0, PalindromeQ@ m], k += 2]; k], {n, 63}] (* Michael De Vlieger, Oct 30 2017 *)
CROSSREFS
Sequence in context: A336057 A165789 A133090 * A161501 A118273 A242616
KEYWORD
base,nonn
AUTHOR
Leroy Quet, Oct 19 2008
EXTENSIONS
Extended by Ray Chandler, Oct 26 2008
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)