The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A161400 Positive integers that are palindromes (of even length) in binary, each made by concatenating two identical binary palindromes. 1
 3, 15, 45, 63, 153, 255, 561, 693, 891, 1023, 2145, 2925, 3315, 4095, 8385, 9417, 10965, 11997, 12771, 13803, 15351, 16383, 33153, 39321, 42405, 48573, 50115, 56283, 59367, 65535, 131841, 140049, 152361, 160569, 166725, 174933, 187245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If m is the n-th positive integer that is a binary palindrome, and m written in binary is k digits long, then a(n) = m*(2^k +1). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..10000 FORMULA a(n) = (2^A070939(p)+1)*p where p = A006995(n+1). [From R. J. Mathar, Sep 27 2009] EXAMPLE The first eight terms of this sequence written in binary: 11, 1111, 101101, 111111, 10011001, 11111111, 1000110001, 1010110101. MATHEMATICA Union[Flatten[Table[FromDigits[Join[#, #], 2]&/@Select[Tuples[ {1, 0}, n], First[ #]!=0&&Last[#]!=0&&#==Reverse[#]&], {n, 10}]]] (* Harvey P. Dale, Jul 15 2014 *) PROG (Python) from itertools import product def bin_pals():   yield "1"   digits, midrange = 2, [[""], ["0", "1"]]   while True:     for p in product("01", repeat=digits//2-1):       left = "1"+"".join(p)       for middle in midrange[digits%2]:         yield left+middle+left[::-1]     digits += 1 def aupton(terms):   alst, bgen = [], bin_pals()   while len(alst) < terms: b = next(bgen); alst.append(int(b+b, 2))   return alst print(aupton(37)) # Michael S. Branicky, Mar 15 2021 CROSSREFS Cf. A006995. Sequence in context: A127407 A196237 A177146 * A112810 A334078 A094191 Adjacent sequences:  A161397 A161398 A161399 * A161401 A161402 A161403 KEYWORD base,nonn AUTHOR Leroy Quet, Jun 09 2009 EXTENSIONS Extended beyond 693 by R. J. Mathar, Sep 27 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 26 10:35 EDT 2021. Contains 346294 sequences. (Running on oeis4.)