A004753 -id:A004753 - cp's OEIS frontend

A107911 Numbers having consecutive zeros and also consecutive ones in binary representation.

12, 19, 24, 25, 28, 35, 38, 39, 44, 48, 49, 50, 51, 52, 56, 57, 60, 67, 70, 71, 75, 76, 77, 78, 79, 83, 88, 89, 92, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 108, 112, 113, 114, 115, 116, 120, 121, 124, 131, 134, 135, 139, 140, 141, 142, 143, 147, 150, 151, 152

Offset: 1

Reinhard Zumkeller, May 28 2005

Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for 2-automatic sequences.

Intersection of A004753 and A004780.
Complement of A107909.
Cf. A007088, A107907.

czcoQ[n_]:=Module[{c2=Partition[IntegerDigits[n,2],2,1]},MemberQ[c2,{0,0}]&&MemberQ[c2,{1,1}]]; Select[Range[200],czcoQ] (* Harvey P. Dale, Jul 24 2012 *)

def ok(n): b = bin(n)[2:]; return "00" in b and "11" in b
print([k for k in range(153) if ok(k)]) # Michael S. Branicky, Dec 19 2021

Offset changed to 1 by Michael S. Branicky, Dec 19 2021

A300302 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number whose binary representation contains the binary representation of n as a substring.

Original entry on oeis.org

1, 2, 2, 3, 4, 3, 4, 6, 5, 4, 5, 8, 7, 6, 5, 6, 10, 9, 11, 8, 6, 7, 12, 11, 12, 12, 9, 7, 8, 14, 13, 13, 16, 13, 10, 8, 9, 16, 15, 14, 20, 17, 14, 11, 9, 10, 18, 17, 23, 22, 21, 18, 15, 12, 10, 11, 20, 19, 24, 28, 24, 22, 19, 19, 13, 11, 12, 22, 21, 25, 32, 29

Offset: 1

Rémy Sigrist, Mar 08 2018

Each positive number k appears A122953(k) times in this array.

			Square array begins:
  n\k|    1    2    3    4    5    6    7    8    9   10
  ---+--------------------------------------------------
    1|    1    2    3    4    5    6    7    8    9   10  <--  A000027
    2|    2    4    5    6    8    9   10   11   12   13  <--  A062289
    3|    3    6    7   11   12   13   14   15   19   22  <--  A004780
    4|    4    8    9   12   16   17   18   19   20   24  <--  A004753
    5|    5   10   11   13   20   21   22   23   26   27  <--  A004748
    6|    6   12   13   14   22   24   25   26   27   28  <--  A004749
    7|    7   14   15   23   28   29   30   31   39   46  <--  A004781
    8|    8   16   17   24   32   33   34   35   40   48  <--  A004779
    9|    9   18   19   25   36   37   38   39   41   50
   10|   10   20   21   26   40   41   42   43   52   53  <--  A132782

Rémy Sigrist, Perl program for A300302

Cf. A000027, A004748, A004749, A004753, A004779, A004780, A004781, A062289, A122953, A132782.

Perl
```
See Links section.
```

T(n, 1) = n.
T(n, 2) = 2*n.
T(n, 3) = 2*n + 1.
T(1, n) = A000027(n).
T(2, n) = A062289(n).
T(3, n) = A004780(n).
T(4, n) = A004753(n).
T(5, n) = A004748(n).
T(6, n) = A004749(n).
T(7, n) = A004781(n).
T(8, n) = A004779(n-1).
T(10, n) = A132782(n).

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A107911 Numbers having consecutive zeros and also consecutive ones in binary representation.

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A300302 Square array T(n, k) (n >= 1, k >= 1) read by antidiagonals upwards: T(n, k) is the k-th positive number whose binary representation contains the binary representation of n as a substring.

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