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A030308 Triangle T(n, k): Write n in base 2, reverse order of digits, to get the n-th row. 211
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
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
T(n, k) = (n // 2^k) mod 2, for 0 <= k <= log[2](n) and n > 0; T(0, 0) = 0. ('//' denotes integer division). - Peter Luschny, Apr 20 2023
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
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 March 19 06:25 EDT 2024. Contains 370953 sequences. (Running on oeis4.)