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