|
%I #12 Apr 30 2015 21:44:24
%S 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,
%T 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,
%U 69,406,1,3,10,7,11,13,17,19,23,29,465
%N 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.
%C 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), ...
%H Antti Karttunen, <a href="/A257253/b257253.txt">Table of n, a(n) for n = 1..3321; the first 81 antidiagonals of the array</a>
%F A(row,col) = (1/2) * (A083221(row,col+1) - A083221(row,col)).
%F A(row,col) = A257251(row,col)/2.
%e The top left corner of the array:
%e 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
%e 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3
%e 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10, 5, 10
%e 21, 14, 7, 14, 7, 14, 21, 7, 21, 14, 7, 14, 7, 14, 21
%e 55, 11, 22, 11, 22, 33, 11, 33, 22, 11, 22, 33, 33, 11, 33
%e 78, 26, 13, 26, 39, 13, 39, 26, 13, 26, 39, 39, 13, 39, 26
%e 136, 17, 34, 51, 17, 51, 34, 17, 34, 51, 51, 17, 51, 34, 17
%e 171, 38, 57, 19, 57, 38, 19, 38, 57, 57, 19, 57, 38, 19, 57
%e 253, 69, 23, 69, 46, 23, 46, 69, 69, 23, 69, 46, 23, 69, 46
%e 406, 29, 87, 58, 29, 58, 87, 87, 29, 87, 58, 29, 87, 58, 87
%e 465, 93, 62, 31, 62, 93, 93, 31, 93, 62, 31, 93, 62, 93, 124
%e 666, 74, 37, 74, 111, 111, 37, 111, 74, 37, 111, 74, 111, 148, 74
%e 820, 41, 82, 123, 123, 41, 123, 82, 41, 123, 82, 123, 164, 82, 41
%e 903, 86, 129, 129, 43, 129, 86, 43, 129, 86, 129, 172, 86, 43, 86
%e 1081, 141, 141, 47, 141, 94, 47, 141, 94, 141, 188, 94, 47, 94, 47
%e 1378, 159, 53, 159, 106, 53, 159, 106, 159, 212, 106, 53, 106, 53, 106
%e ...
%o (Scheme)
%o (define (A257253 n) (A257253bi (A002260 n) (A004736 n)))
%o (define (A257253bi row col) (* (/ 1 2) (- (A083221bi row (+ 1 col)) (A083221bi row col)))) ;; Code for A083221bi given in A083221.
%Y Transpose: A257254.
%Y Cf. A083221, A257251 (same array but with terms multiplied by 2).
%Y Column 1: A008837.
%Y Row 4: (7/2) * A145011.
%K nonn,tabl
%O 1,3
%A _Antti Karttunen_, Apr 29 2015
|
