cp's OEIS Frontend

A105027 Write numbers in binary under each other; to get the next block of 2^k (k >= 0) terms of the sequence, start at 2^k, read diagonals in upward direction and convert to decimal.

%I A105027 #32 Apr 18 2022 22:33:10
%S A105027 0,1,3,2,6,5,4,7,15,10,9,8,11,14,13,12,28,23,18,17,16,19,22,21,20,31,
%T A105027 26,25,24,27,30,29,61,44,39,34,33,32,35,38,37,36,47,42,41,40,43,46,45,
%U A105027 60,55,50,49,48,51,54,53,52,63,58,57,56,59,62,126,93,76,71,66,65,64,67,70
%N A105027 Write numbers in binary under each other; to get the next block of 2^k (k >= 0) terms of the sequence, start at 2^k, read diagonals in upward direction and convert to decimal.
%C A105027 This is a permutation of the nonnegative integers.
%C A105027 Structure: blocks of size 2^k - 1 taken from A102370, interspersed with terms of A102371. - _Philippe Deléham_, Nov 17 2007
%C A105027 a(A062289(n)) = A102370(n) for n > 0; a(A000225(n)) = A102371(n); a(A214433(n)) = A105025(a(n)). - _Reinhard Zumkeller_, Jul 21 2012
%H A105027 Reinhard Zumkeller, <a href="/A105027/b105027.txt">Table of n, a(n) for n = 0..10000</a>
%H A105027 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].
%H A105027 David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.
%H A105027 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A105027 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A105027 a(2^n - 1) = A102371(n) for n > 0. - _Philippe Deléham_, May 10 2005
%e A105027         0
%e A105027         1
%e A105027        10
%e A105027        11
%e A105027    -> 100  Starting here, the upward diagonals
%e A105027       101  read 110, 101, 100, 111, giving the block 6, 5, 4, 7.
%e A105027       110
%e A105027       111
%e A105027      1000
%e A105027      1001
%e A105027      1010
%e A105027      1011
%e A105027       ...
%t A105027 block[k_] := Module[{t}, t = Table[PadLeft[IntegerDigits[n, 2], k+1], {n, 2^(k-1), 2^(k+1)-1}]; Table[FromDigits[Table[t[[n-m+1, m]], {m, 1, k+1}], 2], {n,2^(k-1)+1, 2^(k-1)+2^k}]]; block[0] = {0, 1}; Table[block[k], {k, 0, 6}] // Flatten (* _Jean-François Alcover_, Jun 30 2015 *)
%o A105027 (Haskell)
%o A105027 import Data.Bits ((.|.), (.&.))
%o A105027 a105027 n = foldl (.|.) 0 $ zipWith (.&.)
%o A105027                   a000079_list $ enumFromTo (n + 1 - a070939 n) n
%o A105027 -- _Reinhard Zumkeller_, Jul 21 2012
%o A105027 (PARI) apply( {A105027(n,L=exponent(n+!n))=sum(k=0,L,bitand(n+k-L,2^k))}, [0..55]) \\ _M. F. Hasler_, Apr 18 2022
%Y A105027 Cf. A102370, A105025, A105026, A105028.
%Y A105027 Cf. A070939, A000079.
%Y A105027 Cf. A214414 (fixed points), A214417 (inverse).
%K A105027 nonn,nice,base
%O A105027 0,3
%A A105027 _N. J. A. Sloane_, Apr 03 2005
%E A105027 More terms from _John W. Layman_, Apr 07 2005