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.
%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