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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.
9
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
1,2
FORMULA
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)).
EXAMPLE
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
PROG
(Scheme)
(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))))
CROSSREFS
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.
Sequence in context: A132665 A255122 A191445 * A132667 A133729 A244987
KEYWORD
nonn,tabl,base
AUTHOR
Antti Karttunen, Nov 03 2016
STATUS
approved