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

1,3

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), ...

Links

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

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

Adjacent sequences: A257250 A257251 A257252 * A257254 A257255 A257256

Keyword

nonn,tabl

Author

Antti Karttunen, Apr 29 2015

Status

approved