# discrete math- sequence question

#### s3b4k

Joined Feb 15, 2010
38
I need to come up with a rule or a formula for the following:

1,2,2,2,3,3,3,3,3,5,5,5,5,5,5,5.....

Joined Jul 7, 2009
1,583
Hint: 2*n + 1 and primes

#### jpanhalt

Joined Jan 18, 2008
11,088
There may be more than one pattern that gives that initial sequence. One solution is: the digits 1,2,3,and 5 are primes (positive). The repeat frequencies seem to follow just the odd numbers. The next three repeat frequencies would be 9, 11 and 13. That is, the next two sequences would be nine 7's, then eleven 11's.

John

#### s3b4k

Joined Feb 15, 2010
38
ok thanks a lot for the help, but is there an exact formula i can use, or is it only solvable by explaining it?

#### Markd77

Joined Sep 7, 2009
2,806
1 isn't normally considered a prime if that makes any difference.

#### Markd77

Joined Sep 7, 2009
2,806
I searched for the sequence on google and found this. Still no idea what it is.
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list.
(a) 3, 6, 11, 18, 27, 38, 51, 66, 83,
(b) 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8,

#### jpanhalt

Joined Jan 18, 2008
11,088
For (b) the sequence starts with 1, and if there are at least 2 previous term, then the subsequent term is the sum of the previous two terms, otherwise it is 2 (or alternatively, the previous term is doubled). The replicates of each term is as in the first problem.

I am too tired to look at (a) now. Perhaps this question should have its own thread.

John

Edit: For (a) here's a reference: http://mathworld.wolfram.com/Near-SquarePrime.html

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#### s3b4k

Joined Feb 15, 2010
38
this question is driving me nuts, are the next three terms going to be 8,8,8 or 7,7,7. because it good either be prime numbers or just the sum of the previous numbers, but if its the sum of the previous numbers how do you get the two there

#### jpanhalt

Joined Jan 18, 2008
11,088
this question is driving me nuts, are the next three terms going to be 8,8,8 or 7,7,7. because it good either be prime numbers or just the sum of the previous numbers, but if its the sum of the previous numbers how do you get the two there
There is not enough information to know for sure. The sum of the previous numbers (Fibonacci, 8) may be what your teacher wants. In either case, you have to make an explanation for the first number (or absence thereof).

John

PS, when I went to school 1 was still prime. But then, it was a public school.