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 A274913 #12 Nov 14 2016 13:12:46
%S A274913 1,2,3,1,4,1,2,3,2,3,1,4,1,4,1,2,3,2,3,2,3,1,4,1,4,1,4,1,2,3,2,3,2,3,
%T A274913 2,3,1,4,1,4,1,4,1,4,1,2,3,2,3,2,3,2,3,2,3,1,4,1,4,1,4,1,4,1,4,1,2,3,
%U A274913 2,3,2,3,2,3,2,3,2,3,1,4,1,4,1,4,1,4,1,4,1,4,1,2,3,2,3,2,3,2,3,2,3,2,3,2,3
%N A274913 Square array read by antidiagonals upwards in which each new term is the least positive integer distinct from its neighbors.
%C A274913 This is also a triangle read by rows in which each new term is the least positive integer distinct from its neighbors.
%C A274913 In the square array we have that:
%C A274913 Antidiagonal sums give the positive terms of A008851.
%C A274913 Odd-indexed rows give A010684.
%C A274913 Even-indexed rows give A010694.
%C A274913 Odd-indexed columns give A000034.
%C A274913 Even-indexed columns give A010702.
%C A274913 Odd-indexed antidiagonals give the initial terms of A010685.
%C A274913 Even-indexed antidiagonals give the initial terms of A010693.
%C A274913 Main diagonal gives A010685.
%C A274913 This is also a triangle read by rows in which each new term is the least positive integer distinct from its neighbors.
%C A274913 In the triangle we have that:
%C A274913 Row sums give the positive terms of A008851.
%C A274913 Odd-indexed columns give A000034.
%C A274913 Even-indexed columns give A010702.
%C A274913 Odd-indexed diagonals give A010684.
%C A274913 Even-indexed diagonals give A010694.
%C A274913 Odd-indexed rows give the initial terms of A010685.
%C A274913 Even-indexed rows give the initial terms of A010693.
%C A274913 Odd-indexed antidiagonals give the initial terms of A010684.
%C A274913 Even-indexed antidiagonals give the initial terms of A010694.
%F A274913 a(n) = A274912(n) + 1.
%e A274913 The corner of the square array begins:
%e A274913 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, ...
%e A274913 2, 4, 2, 4, 2, 4, 2, 4, 2, ...
%e A274913 1, 3, 1, 3, 1, 3, 1, 3, ...
%e A274913 2, 4, 2, 4, 2, 4, 2, ...
%e A274913 1, 3, 1, 3, 1, 3, ...
%e A274913 2, 4, 2, 4, 2, ...
%e A274913 1, 3, 1, 3, ...
%e A274913 2, 4, 2, ...
%e A274913 1, 3, ...
%e A274913 2, ...
%e A274913 ...
%e A274913 The sequence written as a triangle begins:
%e A274913 1;
%e A274913 2, 3;
%e A274913 1, 4, 1;
%e A274913 2, 3, 2, 3;
%e A274913 1, 4, 1, 4, 1;
%e A274913 2, 3, 2, 3, 2, 3;
%e A274913 1, 4, 1, 4, 1, 4, 1;
%e A274913 2, 3, 2, 3, 2, 3, 2, 3;
%e A274913 1, 4, 1, 4, 1, 4, 1, 4, 1;
%e A274913 2, 3, 2, 3, 2, 3, 2, 3, 2, 3;
%e A274913 ...
%t A274913 Table[1 + Boole@ EvenQ@ # + 2 Boole@ EvenQ@ k &[n - k + 1], {n, 14}, {k, n}] // Flatten (* _Michael De Vlieger_, Nov 14 2016 *)
%Y A274913 Cf. A000034, A008851, A010684, A010685, A010693, A010694, A010702, A274912, A274921.
%K A274913 nonn,tabl
%O A274913 1,2
%A A274913 _Omar E. Pol_, Jul 11 2016