cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A323674 #32 Feb 05 2019 21:03:46
%S A323674 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,
%T A323674 31,22,19,21,27,35,37,37,35,27,21,24,29,42,41,48,41,42,29,24,26,34,46,
%U A323674 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
%N 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.
%C A323674 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.
%F A323674 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.
%e A323674 Square array begins:
%e A323674    4,   6,   9,  11,  14,  16,  19,  21,  24,  26, ...
%e A323674    6,   8,  13,  15,  20,  22,  27,  29,  34,  36, ...
%e A323674    9,  13,  20,  24,  31,  35,  42,  46,  53,  57, ...
%e A323674   11,  15,  24,  28,  37,  41,  50,  54,  63,  67, ...
%e A323674   14,  20,  31,  37,  48,  54,  65,  71,  82,  88, ...
%e A323674   16,  22,  35,  41,  54,  60,  73,  79,  92,  98, ...
%e A323674   19,  27,  42,  50,  65,  73,  88,  96, 111, 119, ...
%e A323674   21,  29,  46,  54,  71,  79,  96, 104, 121, 129, ...
%e A323674   24,  34,  53,  63,  82,  92, 111, 121, 140, 150, ...
%e A323674   26,  36,  57,  67,  88,  98, 119, 129, 150, 160, ...
%e A323674   ...
%e A323674 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.
%o A323674 (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);
%o A323674 matrix(7, 7, n, k, a(n, k)) \\ _Michel Marcus_, Jan 25 2019
%Y A323674 The first and second rows are A047209 and A047336.
%Y A323674 The diagonal is A062717, the numbers x for which 6*x + 1 is a perfect square.
%K A323674 nonn,tabl,easy
%O A323674 1,1
%A A323674 _Sally Myers Moite_, Jan 23 2019