The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A297405 Binary "cubes"; numbers whose binary representation consists of three consecutive identical blocks. 3
 7, 42, 63, 292, 365, 438, 511, 2184, 2457, 2730, 3003, 3276, 3549, 3822, 4095, 16912, 17969, 19026, 20083, 21140, 22197, 23254, 24311, 25368, 26425, 27482, 28539, 29596, 30653, 31710, 32767, 133152, 137313, 141474, 145635, 149796, 153957, 158118, 162279, 166440, 170601, 174762, 178923, 183084, 187245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Alternatively, numbers of the form k*(4^n + 2^n + 1), where 2^(n-1) <= k < 2^n. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Daniel M. Kane, Carlo Sanna, and Jeffrey Shallit, Waring's Theorem for Binary Powers, arXiv:1801.04483 [math.NT], 2018. FORMULA a(n) = n*(1 + 2^p + 4^p) with p = 1 + floor(log_2(n)). - Alois P. Heinz, Dec 29 2017 G.f.: (7*x + Sum_{n>=1} (4^n + 3*8^n + (2^n + 2*4^n - 3*8^n)*x)*x^(2^n))/(1-x)^2. - Robert Israel, Dec 31 2017 EXAMPLE 42 in base 2 is 101010, which consists of three copies of the block "10". MAPLE a:= n-> (p-> n*(1+2^p+4^p))(1+ilog2(n)): seq(a(n), n=1..50); # Alois P. Heinz, Dec 29 2017 MATHEMATICA bc[n_]:=FromDigits[Join[n, n, n], 2]; Flatten[Table[bc/@Select[Tuples[ {1, 0}, n], #[[1]] == 1&], {n, 6}]]//Union (* Harvey P. Dale, Oct 09 2021 *) PROG (Python) def a(n): return int(bin(n)[2:]*3, 2) print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Jul 04 2022 # Alternative: def A297405(n): p = n.bit_length() return n * (1 + 2**p + 4**p) print([A297405(n) for n in range(1, 46)]) # Peter Luschny, Jul 05 2022 (PARI) a(n) = n=binary(n); fromdigits(concat([n, n, n]) , 2) \\ Iain Fox, Jul 04 2022 CROSSREFS Cf. A020330, which is the corresponding sequence for squares. Subsequence of A121016. Sequence in context: A188066 A225327 A102532 * A044109 A195320 A110451 Adjacent sequences: A297402 A297403 A297404 * A297406 A297407 A297408 KEYWORD nonn,base AUTHOR Jeffrey Shallit, Dec 29 2017 STATUS approved

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

Last modified December 8 03:48 EST 2022. Contains 358672 sequences. (Running on oeis4.)