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A323674
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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PROG
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(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);
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CROSSREFS
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The diagonal is A062717, the numbers x for which 6*x + 1 is a perfect square.
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KEYWORD
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AUTHOR
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STATUS
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approved
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