A277881 -id:A277881 - cp's OEIS frontend

A277880 Dispersion of evil numbers: Square array A(r,c) with A(r,1) = A000069(r); and for c > 1, A(r,c) = A001969(1+(A(r,c-1))), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

1, 3, 2, 6, 5, 4, 12, 10, 9, 7, 24, 20, 18, 15, 8, 48, 40, 36, 30, 17, 11, 96, 80, 72, 60, 34, 23, 13, 192, 160, 144, 120, 68, 46, 27, 14, 384, 320, 288, 240, 136, 92, 54, 29, 16, 768, 640, 576, 480, 272, 184, 108, 58, 33, 19, 1536, 1280, 1152, 960, 544, 368, 216, 116, 66, 39, 21, 3072, 2560, 2304, 1920, 1088, 736, 432, 232, 132, 78, 43, 22

Offset: 1

Antti Karttunen, Nov 03 2016

			The top left 12 x 12 corner of the array:
   1,  3,  6,  12,  24,  48,   96,  192,  384,   768,  1536,  3072
   2,  5, 10,  20,  40,  80,  160,  320,  640,  1280,  2560,  5120
   4,  9, 18,  36,  72, 144,  288,  576, 1152,  2304,  4608,  9216
   7, 15, 30,  60, 120, 240,  480,  960, 1920,  3840,  7680, 15360
   8, 17, 34,  68, 136, 272,  544, 1088, 2176,  4352,  8704, 17408
  11, 23, 46,  92, 184, 368,  736, 1472, 2944,  5888, 11776, 23552
  13, 27, 54, 108, 216, 432,  864, 1728, 3456,  6912, 13824, 27648
  14, 29, 58, 116, 232, 464,  928, 1856, 3712,  7424, 14848, 29696
  16, 33, 66, 132, 264, 528, 1056, 2112, 4224,  8448, 16896, 33792
  19, 39, 78, 156, 312, 624, 1248, 2496, 4992,  9984, 19968, 39936
  21, 43, 86, 172, 344, 688, 1376, 2752, 5504, 11008, 22016, 44032
  22, 45, 90, 180, 360, 720, 1440, 2880, 5760, 11520, 23040, 46080

Inverse permutation: A277881.
Transpose: A277882.
Column 1: A000069, column 2: A129771.
Row 1: A003945.
Cf. A277813 (index of the row where n is located in this array), A277822 (index of the column).
Cf. A001969.
Other related tables or permutations: A277820, A277902, A248513.

(define (A277880 n) (A277880bi (A002260 n) (A004736 n)))
(define (A277880bi row col) (if (= 1 col) (A000069 row) (A001969 (+ 1 (A277880bi row (- col 1))))))
;; Alternatively:
(define (A277880bi row col) (cond ((= 1 col) (A000069 row)) ((= 2 col) (A129771 row)) (else (* 2 (A277880bi row (- col 1))))))
(define (A129771 n) (+ 1 (* 2 (A000069 n))))

A(r,1) = A000069(r) and for c > 1, A(r,c) = A001969(1+(A(r,c-1))).
Alternatively, if we set also the second column explicitly as:
   A(r,2) = A129771(r) = 1+ 2*A000069(r),
then the rest of entries in each row are obtained just by doubling the preceding term on the same row: A(r,c) = 2*A(r,c-1), for c >= 3.
As a composition of other permutations:
a(n) = A277902(A277820(n)).

A277901 If A010060(n) = 1, a(n) = A065621(A115384(n)), otherwise a(n) = A048724(a(floor(n/2))).

Original entry on oeis.org

1, 2, 3, 7, 6, 5, 4, 13, 9, 10, 14, 15, 11, 8, 12, 25, 23, 27, 26, 30, 31, 28, 18, 17, 21, 22, 29, 19, 24, 20, 16, 49, 43, 57, 50, 45, 55, 52, 46, 34, 61, 62, 33, 59, 36, 54, 56, 51, 41, 42, 63, 47, 58, 39, 44, 37, 53, 40, 38, 60, 35, 32, 48, 97, 83, 125, 98, 75, 103, 100, 86, 119, 109, 110, 89, 107, 92, 114

Offset: 1

Antti Karttunen, Nov 03 2016

a(n) gives the number that is in the same position in array A277820 as where n is located in array A277880.

			The top left corner of array A277880 is:
   1,  3,  6, 12
   2,  5, 10, 20
   4,  9, 18, 36
   7, 15, 30, 60
   8, 17, 34, 68
while the top left corner of A277820 is:
   1,  3,  5, 15
   2,  6, 10, 30
   7,  9, 27, 45
   4, 12, 20, 60
  13, 23, 57, 75
thus a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 7, a(5) = 6, a(6) = 5, a(7) = 4, a(8) = 13, a(9) = 9, a(12) = 15 and a(15) = 12.

Inverse: A277902.
Cf. A000069, A001969, A010060, A048724, A065621, A115384, A129771, A277823, A277825.
Related permutations and arrays: A277820, A277880, A277881.

If A010060(n) = 1 [when n is one of the odious numbers, A000069], then a(n) = A065621(A115384(n)), otherwise a(n) = A048724(a(floor(n/2))).
As a composition of other permutations:
a(n) = A277820(A277881(n)).
Other identities. For all n >= 1:
A010060(a(n)) = A010060(n). [Preserves the parity of binary weight.]
a(A000069(n)) = A065621(n).
a(A003945(n)) = A001317(n).
a(A129771(n)) = A277823(n).
a(2*A129771(n)) = A277825(n).

cp's OEIS Frontend

A277880 Dispersion of evil numbers: Square array A(r,c) with A(r,1) = A000069(r); and for c > 1, A(r,c) = A001969(1+(A(r,c-1))), read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Scheme

Formula