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 A274913 Square array read by antidiagonals upwards in which each new term is the least positive integer distinct from its neighbors. 5
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is also a triangle read by rows in which each new term is the least positive integer distinct from its neighbors. In the square array we have that: Antidiagonal sums give the positive terms of A008851. Odd-indexed rows give A010684. Even-indexed rows give A010694. Odd-indexed columns give A000034. Even-indexed columns give A010702. Odd-indexed antidiagonals give the initial terms of A010685. Even-indexed antidiagonals give the initial terms of A010693. Main diagonal gives A010685. This is also a triangle read by rows in which each new term is the least positive integer distinct from its neighbors. In the triangle we have that: Row sums give the positive terms of A008851. Odd-indexed columns give A000034. Even-indexed columns give A010702. Odd-indexed diagonals give A010684. Even-indexed diagonals give A010694. Odd-indexed rows give the initial terms of A010685. Even-indexed rows give the initial terms of A010693. Odd-indexed antidiagonals give the initial terms of A010684. Even-indexed antidiagonals give the initial terms of A010694. LINKS FORMULA a(n) = A274912(n) + 1. EXAMPLE The corner of the square array begins: 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, ... 2, 4, 2, 4, 2, 4, 2, 4, 2, ... 1, 3, 1, 3, 1, 3, 1, 3, ... 2, 4, 2, 4, 2, 4, 2, ... 1, 3, 1, 3, 1, 3, ... 2, 4, 2, 4, 2, ... 1, 3, 1, 3, ... 2, 4, 2, ... 1, 3, ... 2, ... ... The sequence written as a triangle begins: 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, 2, 3; 1, 4, 1, 4, 1, 4, 1, 4, 1; 2, 3, 2, 3, 2, 3, 2, 3, 2, 3; ... MATHEMATICA Table[1 + Boole@ EvenQ@ # + 2 Boole@ EvenQ@ k &[n - k + 1], {n, 14}, {k, n}] // Flatten (* Michael De Vlieger, Nov 14 2016 *) CROSSREFS Cf. A000034, A008851, A010684, A010685, A010693, A010694, A010702, A274912, A274921. Sequence in context: A055445 A135560 A138967 * A330761 A265105 A035612 Adjacent sequences:  A274910 A274911 A274912 * A274914 A274915 A274916 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Jul 11 2016 STATUS approved

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Last modified June 4 11:09 EDT 2020. Contains 334825 sequences. (Running on oeis4.)