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For example, in triangular numbers $1, 3, 6, 10, 15, 21, 28, 36, 45, 55\dots$, two evens come after two odds. I want something like it for three odds and three evens.

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closed as too broad by BaronVT, vadim123, Nicholas R. Peterson, Jesko Hüttenhain, Jack D'Aurizio Jan 10 at 18:36

There are either too many possible answers, or good answers would be too long for this format. Please add details to narrow the answer set or to isolate an issue that can be answered in a few paragraphs.If this question can be reworded to fit the rules in the help center, please edit the question.

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Does '1, 3, 5, 2, 4, 6, 7, 9, 11, 8, 10, 12, ...' not satisfy your constraint? Without knowing more about what you need it's impossible to give a good answer to this question. –  Steven Stadnicki Jan 10 at 17:31
    
well, 3,5,7,4,6,8,2,2,2,2,2 etc. (all 2s) This is just to say: Any sequence is mathematically logically, see comments here: math.stackexchange.com/questions/632321/… –  Bernd Jan 10 at 17:31

1 Answer 1

up vote 5 down vote accepted

The sequence $a_n = \lceil n/3\rceil$ works.

The notation $\lceil m \rceil$ indicates the smallest integer not greater than $m$ (the "ceiling"). So the sequence for $n = 1, 2, 3, ...$ is $a_n = 1, 1, 1, 2, 2, 2, 3, 3, 3, ...$

Or, the more technical name for this sequence is the positive integers repeated three times. (Which is actually an incorrect name, as each integer is repeated just twice; it's written, it's repeated, and it's repeated a second time. But who's counting?)

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I dont understand an and floor here. Please write like this 1,2,3,4,.... –  Waqar Ahmad Jan 10 at 17:38
    
Actually I just changed it to ceiling because $n$ are the natural numbers (usually). –  John Jan 10 at 17:39
    
I edited my answer. –  John Jan 10 at 17:42

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