A323674 Square array, read by antidiagonals, of the positive integers 6cd +-c +-d = (6c +- 1)d +- c. Alternate rows (or columns) are numbers that differ by c from multiples of 6c - 1 or 6c + 1.

4, 6, 6, 9, 8, 9, 11, 13, 13, 11, 14, 15, 20, 15, 14, 16, 20, 24, 24, 20, 16, 19, 22, 31, 28, 31, 22, 19, 21, 27, 35, 37, 37, 35, 27, 21, 24, 29, 42, 41, 48, 41, 42, 29, 24, 26, 34, 46, 50, 54, 54, 50, 46, 34, 26, 29, 36, 53, 54, 65, 60, 65, 54, 53, 36, 29, 31, 41, 57, 63, 71, 73, 73, 71, 63, 57, 41, 31

Offset: 1

Author

Sally Myers Moite, Jan 23 2019

Keywords

• nonn
• tabl
• easy

Comments

This sequence without duplicates is A067611, which is the complement of A002822, the positive integers x for which 6x - 1 and 6x + 1 are twin primes.

Examples

			Square array begins:
   4,   6,   9,  11,  14,  16,  19,  21,  24,  26, ...
   6,   8,  13,  15,  20,  22,  27,  29,  34,  36, ...
   9,  13,  20,  24,  31,  35,  42,  46,  53,  57, ...
  11,  15,  24,  28,  37,  41,  50,  54,  63,  67, ...
  14,  20,  31,  37,  48,  54,  65,  71,  82,  88, ...
  16,  22,  35,  41,  54,  60,  73,  79,  92,  98, ...
  19,  27,  42,  50,  65,  73,  88,  96, 111, 119, ...
  21,  29,  46,  54,  71,  79,  96, 104, 121, 129, ...
  24,  34,  53,  63,  82,  92, 111, 121, 140, 150, ...
  26,  36,  57,  67,  88,  98, 119, 129, 150, 160, ...
  ...
Note that, for example, the third row (or column) contains numbers that differ by 2 from multiples of 11 = 6*2 - 1, and the eighth row contains numbers that differ by 4 from multiples of 25 = 6*4 + 1.
		

Crossrefs

The first and second rows are A047209 and A047336.

The diagonal is A062717, the numbers x for which 6*x + 1 is a perfect square.

Programs

PARI

a(m,n) = 6*floor((m+1)/2)*floor((n+1)/2) + ((-1)^n)*floor((m+1)/2) + ((-1)^m)*floor((n+1)/2);
matrix(7, 7, n, k, a(n, k)) \\ Michel Marcus, Jan 25 2019

Formula

a(m,n) = 6*floor((m+1)/2)*floor((n+1)/2) + ((-1)^n)*floor((m+1)/2) + ((-1)^m)*floor((n+1)/2), m,n >= 1.