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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

Table of n, a(n) for n=1..105.

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 * A265105 A035612 A199539

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 February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)