next number
 

Hi Mersenneforum,

Find the next number in the sequence -

3, 5, 8, 13, 22, ?

There are a few ways to go with this , but here is some Maple computer code -

[SPOILER]a := Vector[row](9)
a[1] := 3; for i from 2 to 9 do a[i] := 2*a[i-1]-i+1 end do
a
***** end Maple code *****
[3,5,8,13,22,39 ... ]

[/SPOILER]

Regards,
Matt

[QUOTE=MattcAnderson;445603]Hi Mersenneforum,

Find the next number in the sequence -

3, 5, 8, 13, 22, ?

There are a few ways to go with this , but here is some Maple computer code -

....

Regards,
Matt[/QUOTE]


without the hint there's always multiple possible ways to continue a sequence so it kind of is redundant. for example one pattern possibility is that we add a fibonacci numbers to the previous term as we go after an initial 0 to get our different 3+0 5+0, 8+1, 13+1, which would lead to 36, we could use a sequence of difference attempt and get:

3,5,8,13,22
2,3,5,9 - first difference
1,2,4 - second difference. the second difference pattern is potentially powers of 2 that leads to a first difference of 17 which gets to 39. etc.

39 if these are [SPOILER]Number of steps to reach 0 when starting from 2^n and iterating the map x -> x - (number of 1's in binary representation of x)[/SPOILER]
39 if these are [SPOILER]a(n) = 1 + 2^(n-1) + n[/SPOILER]
37 if these are [SPOILER]Powers of fifth root of 13 rounded up.[/SPOILER]
36 if these are [SPOILER]Number of 1-dimensional sand piles with n grains. [/SPOILER]
36 if these are [SPOILER]Number of typable lambda terms of size n with size 0 for the variables. [/SPOILER]
36 if these are [SPOILER]Floor(Fibonacci(n)/4)[/SPOILER]
36 if these are [SPOILER]Powers of fifth root of 13 rounded to nearest integer[/SPOILER]
36 if these are [SPOILER]Antidiagonal sums of triangle [URL="http://oeis.org/A124428"]A124428[/URL]. [/SPOILER]
36 if these are [SPOILER]Floor(sqrt(F(n+2)^2 + F(n)^2))[/SPOILER]
31 if these are [SPOILER]q-sinh(x) evaluated at q=-x[/SPOILER]
37 if these are [SPOILER]Numbers of Twopins positions.[/SPOILER]

So, take your pick :rolleyes:

[QUOTE=MattcAnderson;445603]Hi Mersenneforum,

Find the next number in the sequence -

3, 5, 8, 13, 22, ?[/QUOTE]42.

Additional possible values, unmentioned before:
28, 30, 32, or 40 (all with "tough logic" behind)

[QUOTE=MattcAnderson;445603]Hi Mersenneforum,

Find the next number in the sequence -

3, 5, 8, 13, 22, ?

[/QUOTE]

It could be any number -- integer, fraction, irrational, transcendental, complex, quarternion, octonion etc -- there are an uncountable number of sequences with those start values. :smile:

[QUOTE=LaurV;445647]Additional possible values, unmentioned before:
28, 30, 32, or 40 (all with "tough logic" behind)[/QUOTE]

even 38 is possible just take the second order difference to be a different pattern like 1 more than the triangular numbers and you get 7 as the next second difference and that leads to 9+7 =16 22+16 =38.

*grinz*
 

Hi ,

Thank you for all the input. Although I didn't read them all. I'm glad we all have this little corner of the internet to communicate. This is a .org website and not a .com . For this I am grateful.

Regards,
Matt hew C A

47

[QUOTE=MattcAnderson;445721]Hi ,

Thank you for all the input. Although I didn't read them all. I'm glad we all have this little corner of the internet to communicate. This is a .org website and not a .com . For this I am grateful.

Regards,
Matt hew C A[/QUOTE]

a note on the code it can be simplified by taking the start index of 0 and starting i from 1 in theory.

Hi math and computer creatures who actually read this webpage,
(Hi all)

I appreciate the input on this next number puzzle. I found this puzzle on the internet. I don't remember where I found it. Happy November 1st to all.

Last night was Halloween here in the U.S.

Regards,
Matt