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 A175468 Those positive integers n such that n = (2^m +1)*k, each for some positive integer m, and k < 2^m. 6
 3, 5, 9, 10, 15, 17, 18, 27, 33, 34, 36, 45, 51, 54, 63, 65, 66, 68, 85, 99, 102, 119, 129, 130, 132, 136, 153, 165, 170, 187, 195, 198, 204, 221, 231, 238, 255, 257, 258, 260, 264, 297, 325, 330, 363, 387, 390, 396, 429, 455, 462, 495, 513, 514, 516, 520, 528 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Written in binary, each term consists of a given series of digits repeated twice, once at the beginning of the number and once at the end, separated by any number of 0's. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Parthasarathy Madhusudan, Dirk Nowotka, Aayush Rajasekaran, Jeffrey Shallit, Lagrange's Theorem for Binary Squares, arXiv:1710.04247 [math.NT] 2017. Aayush Rajasekaran, Using Automata Theory to Solve Problems in Additive Number Theory, MS thesis, University of Waterloo, 2018. EXAMPLE The first few terms written in binary: 11, 101, 1001, 1010, 1111, 10001, 10010, 11011. For instance, a(7) = 18 is 10010 in binary. This binary representation is made up of a 10 (2 in decimal) occurring both at the beginning and the end, with a single 0 between. MAPLE N:= 1000: # to get all terms <= N A:= {seq(seq((2^m+1)*k, k=1..min(2^m-1, floor(N/(2^m+1)))), m=1..ilog2(N-1))}: sort(convert(A, list)); # Robert Israel, Feb 08 2016 MATHEMATICA With[{n = 528}, Union@ Flatten@ Table[(2^m + 1) k, {m, Floor@ Log2[n - 1]}, {k, Min[2^m - 1, Floor[n/(2^m + 1)]]}]] (* Michael De Vlieger, Mar 14 2018 *) CROSSREFS Cf. A175469, A175470. Sequence in context: A153710 A230385 A269399 * A286065 A316296 A063038 Adjacent sequences:  A175465 A175466 A175467 * A175469 A175470 A175471 KEYWORD nonn AUTHOR Leroy Quet, May 24 2010 EXTENSIONS More terms from Jon E. Schoenfield, Jun 13 2010 STATUS approved

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Last modified January 25 01:49 EST 2020. Contains 331229 sequences. (Running on oeis4.)