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.

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

Author

Antti Karttunen, Apr 29 2015

Keywords

• nonn
• tabl

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), ...

Examples

			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
  ...
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..3321; the first 81 antidiagonals of the array

Crossrefs

Transpose: A257254.

Cf. A083221, A257251 (same array but with terms multiplied by 2).

Column 1: A008837.

Row 4: (7/2) * A145011.

Programs

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.

Formula

A(row,col) = (1/2) * (A083221(row,col+1) - A083221(row,col)).

A(row,col) = A257251(row,col)/2.