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 A030308 Triangle T(n, k): Write n in base 2, reverse order of digits, to get the n-th row. 200
 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS This is the quite common, so-called "bittest" function, see Pari code. - M. F. Hasler, Jul 21 2013 For a given number m and a digit position k the corresponding sequence index n can be calculated by n(m, k) = m*(1 + floor(log_2(m))) - 2^(1 + floor(log_2(m))) + k + 1. For example: counted from right to left, the second digit of m = 13 (binary 1101) is '0'. Hence the sequence index is n = n(13, 2) = 39. - Hieronymus Fischer, May 05 2007 A070939(n) is the length of n-th row; A000120(n) is the sum of n-th row; A030101(n) is the n-th row seen as binary number; A000035(n) = T(n, 0). - Reinhard Zumkeller, Jun 17 2012 LINKS Reinhard Zumkeller, Rows n = 0..1023 of triangle, flattened FORMULA a(n) = floor(m/2^(k - 1)) mod 2, where m = max(j|A001855(j) < n) and k = n - A001855(m). - Hieronymus Fischer, May 05 2007, Sep 10 2007 EXAMPLE Triangle begins : 0 1 0, 1 1, 1 0, 0, 1 1, 0, 1 0, 1, 1 1, 1, 1 0, 0, 0, 1 1, 0, 0, 1 - Philippe Deléham, Oct 12 2011 MAPLE A030308_row := n -> op(convert(n, base, 2)): seq(A030308_row(n), n=0..23); # Peter Luschny, Nov 28 2017 MATHEMATICA Flatten[Table[Reverse[IntegerDigits[n, 2]], {n, 0, 23}]] (* T. D. Noe, Oct 12 2011 *) PROG (Haskell) a030308 n k = a030308_tabf !! n !! k a030308_row n = a030308_tabf !! n a030308_tabf = iterate bSucc [0] where    bSucc []       = [1]    bSucc (0 : bs) = 1 : bs    bSucc (1 : bs) = 0 : bSucc bs -- Reinhard Zumkeller, Jun 17 2012 (PARI) A030308(n, k)=bittest(n, k) \\ Assuming that columns are numbered starting with k=0, as suggested by the formula from R. Zumkeller. - M. F. Hasler, Jul 21 2013 (Python) for n in range(20): print([int(z) for z in str(bin(n)[2:])[::-1]]) # Indranil Ghosh, Mar 31 2017 (Sage) A030308_row = lambda n: n.bits() if n > 0 else [0] for n in (0..23): print(A030308_row(n)) # Peter Luschny, Nov 28 2017 (Scala) (0 to 31).map(Integer.toString(_, 2).reverse).mkString.split("").map(Integer.parseInt(_)).toList // Alonso del Arte, Feb 10 2020 CROSSREFS Cf. A030190. Cf. A030341, A030386, A031235, A030567, A031007, A031045, A031087, A031298 for the base-3 to base-10 analogs. Sequence in context: A226520 A268921 A327180 * A280237 A259044 A285383 Adjacent sequences:  A030305 A030306 A030307 * A030309 A030310 A030311 KEYWORD nonn,base,easy,tabf AUTHOR EXTENSIONS Initial 0 and better name by Philippe Deléham, Oct 12 2011 STATUS approved

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Last modified September 19 02:40 EDT 2020. Contains 337175 sequences. (Running on oeis4.)