A284557 -id:A284557 - cp's OEIS frontend

A284555 Positions of zeros in A284557.

0, 3, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 24, 28, 30, 31, 33, 36, 40, 45, 48, 51, 56, 60, 62, 63, 66, 72, 77, 80, 83, 89, 90, 96, 99, 101, 102, 103, 107, 112, 115, 120, 124, 126, 127, 129, 132, 139, 144, 147, 153, 154, 160, 163, 165, 166, 167, 171, 178, 180, 187, 189, 192, 195, 197, 198, 199, 201, 202, 204, 206, 207

Offset: 0

Antti Karttunen, Apr 10 2017

Indexing starts from zero, because a(0) = 0 is a special case in this list.

Antti Karttunen, Table of n, a(n) for n = 0..10000
Index entries for sequences related to binary expansion of n

Cf. A284557, A048727.

Cf. A048717 (a subsequence).

A284270 Square array A(r,c) = A048720(A065621(r), c) mod r, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 3, 4, 4, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 0, 7, 0, 0, 2, 0, 1, 0, 2, 0, 5, 6, 0, 0, 0, 0, 0, 0, 4, 0, 7, 2, 9, 0, 0, 0, 0, 4, 0, 2, 0, 1, 6, 7, 4, 0, 0, 1, 0, 1, 4, 0, 0, 8, 4, 0, 8, 8, 0, 0, 0, 0, 4, 0, 4, 0, 5, 4, 3, 0, 3, 8, 0, 0, 2, 0, 2, 0, 6, 0, 7, 2, 0, 4, 11, 2, 4

Offset: 1

Antti Karttunen, Apr 10 2017

			The top left 17 x 19 corner of the array:
   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   1,  2,  0,  1,  0,  0,  0,  2,  0,  0,  1,  0,  2,  0,  0,  1,  2
   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   3,  1,  3,  2,  2,  1,  0,  4,  1,  4,  2,  2,  1,  0,  0,  3,  1
   2,  4,  0,  2,  0,  0,  0,  4,  0,  0,  2,  0,  4,  0,  0,  2,  4
   4,  1,  1,  2,  4,  2,  0,  4,  6,  1,  6,  4,  1,  0,  0,  1,  5
   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
   7,  5,  7,  1,  8,  5,  7,  2,  2,  7,  2,  1,  1,  5,  0,  4,  6
   6,  2,  6,  4,  4,  2,  0,  8,  2,  8,  4,  4,  2,  0,  0,  6,  2
   9,  7,  0,  3,  0,  0,  5,  6,  0,  0,  8,  0,  1, 10,  0,  1,  0
   4,  8,  0,  4,  0,  0,  0,  8,  0,  0,  4,  0,  8,  0,  0,  4,  8
   8,  3, 11,  6,  0,  9,  3, 12,  7,  0,  8,  5, 12,  6,  0, 11,  0
   8,  2,  2,  4,  8,  4,  0,  8, 12,  2, 12,  8,  2,  0,  0,  2, 10
   4,  8,  8,  1,  5,  1,  1,  2,  4, 10,  8,  2,  4,  2,  0,  4,  6
   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0
  15, 13, 15,  9,  7, 13, 15,  1, 16, 14, 16,  9,  7, 13, 15,  2,  2
  14, 10, 14,  2, 16, 10, 14,  4,  4, 14,  4,  2,  2, 10,  0,  8, 12
  17, 15, 13, 11,  7,  7,  0,  3,  0, 14,  6, 14, 16,  0, 13,  6,  3

Cf. A048720, A065621, A115872, A277320, A284269 (transpose), A284273 (main diagonal), A284552 (column 1).

Row 3: A284557.

(define (A284270 n) (A284270bi (A002260 n) (A004736 n)))
(define (A284270bi row col) (modulo (A277320bi row col) row)) ;; For A277320bi, see in A277320.

A(r,c) = A277320(r,c) mod r = A048720(A065621(r), c) mod r.

A284574 a(n) = A048724(n) mod 3.

Original entry on oeis.org

0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1

Offset: 0

Antti Karttunen, Apr 10 2017

Antti Karttunen, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

Cf. A048724, A284557, A284575.

def A284574(n): return (n^ n<<1)%3 # Chai Wah Wu, Jun 29 2022

(define (A284574 n) (modulo (A048724 n) 3))

a(n) = A048724(n) mod 3.

A284575 a(n) = A048725(n) mod 3.

Original entry on oeis.org

0, 2, 1, 0, 2, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 0, 0, 1, 1, 0

Offset: 0

Antti Karttunen, Apr 10 2017

Antti Karttunen, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

Cf. A048725, A284557, A284574.

(define (A284575 n) (modulo (A048725 n) 3))

a(n) = A048725(n) mod 3.

cp's OEIS Frontend

A284555 Positions of zeros in A284557.

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A284270 Square array A(r,c) = A048720(A065621(r), c) mod r, read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

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A284574 a(n) = A048724(n) mod 3.

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A284575 a(n) = A048725(n) mod 3.

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