login
A257253
Square array A(row,col) = (1/2) * (A083221(row,col+1) - A083221(row,col)): half of the first differences of each row of array constructed from the sieve of Eratosthenes.
4
1, 1, 3, 1, 3, 10, 1, 3, 5, 21, 1, 3, 10, 14, 55, 1, 3, 5, 7, 11, 78, 1, 3, 10, 14, 22, 26, 136, 1, 3, 5, 7, 11, 13, 17, 171, 1, 3, 10, 14, 22, 26, 34, 38, 253, 1, 3, 5, 21, 33, 39, 51, 57, 69, 406, 1, 3, 10, 7, 11, 13, 17, 19, 23, 29, 465
OFFSET
1,3
COMMENTS
The array A(row,col) is read by its downwards antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...
FORMULA
A(row,col) = (1/2) * (A083221(row,col+1) - A083221(row,col)).
A(row,col) = A257251(row,col)/2.
EXAMPLE
The top left corner of the array:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10
21, 14, 7, 14, 7, 14, 21, 7, 21, 14, 7, 14, 7, 14, 21
55, 11, 22, 11, 22, 33, 11, 33, 22, 11, 22, 33, 33, 11, 33
78, 26, 13, 26, 39, 13, 39, 26, 13, 26, 39, 39, 13, 39, 26
136, 17, 34, 51, 17, 51, 34, 17, 34, 51, 51, 17, 51, 34, 17
171, 38, 57, 19, 57, 38, 19, 38, 57, 57, 19, 57, 38, 19, 57
253, 69, 23, 69, 46, 23, 46, 69, 69, 23, 69, 46, 23, 69, 46
406, 29, 87, 58, 29, 58, 87, 87, 29, 87, 58, 29, 87, 58, 87
465, 93, 62, 31, 62, 93, 93, 31, 93, 62, 31, 93, 62, 93, 124
666, 74, 37, 74, 111, 111, 37, 111, 74, 37, 111, 74, 111, 148, 74
820, 41, 82, 123, 123, 41, 123, 82, 41, 123, 82, 123, 164, 82, 41
903, 86, 129, 129, 43, 129, 86, 43, 129, 86, 129, 172, 86, 43, 86
1081, 141, 141, 47, 141, 94, 47, 141, 94, 141, 188, 94, 47, 94, 47
1378, 159, 53, 159, 106, 53, 159, 106, 159, 212, 106, 53, 106, 53, 106
...
PROG
(Scheme)
(define (A257253 n) (A257253bi (A002260 n) (A004736 n)))
(define (A257253bi row col) (* (/ 1 2) (- (A083221bi row (+ 1 col)) (A083221bi row col)))) ;; Code for A083221bi given in A083221.
CROSSREFS
Transpose: A257254.
Cf. A083221, A257251 (same array but with terms multiplied by 2).
Column 1: A008837.
Row 4: (7/2) * A145011.
Sequence in context: A058842 A155734 A128162 * A067329 A170860 A170845
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Apr 29 2015
STATUS
approved