

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
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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.
Oddindexed rows give A010684.
Evenindexed rows give A010694.
Oddindexed columns give A000034.
Evenindexed columns give A010702.
Oddindexed antidiagonals give the initial terms of A010685.
Evenindexed 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.
Oddindexed columns give A000034.
Evenindexed columns give A010702.
Oddindexed diagonals give A010684.
Evenindexed diagonals give A010694.
Oddindexed rows give the initial terms of A010685.
Evenindexed rows give the initial terms of A010693.
Oddindexed antidiagonals give the initial terms of A010684.
Evenindexed 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



