Number sequence

[max4236]

1,2,4,8,15,30,50,100,35,70,286,572,169,338,442,884,437,874,1058,2116?

 

social meduim? music, dancing? :naughty:

[anto]

max could you please elaborate, thanks

[max4236]

I was just watching tap dancing penguins and it made me think of this number sequence for some reason..

 

Imagine two penguins tap dancing on marble tiled floor. They're tapping to a 4/4 beat. The first penguin taps to the drum beat and stays in place. left foot left foot, left right, right left, right right. P1 keep doing that. The second penguin P2 copies the first, only doubles the taps, and then hops to the right one tile at the next 4 count measure. Label the tiles to a line of prime numbers

(1 2 3 5 7 11 13 17 19 23...) and watch their feet.

P1

P2-->

 

Then multiply their feet tap numbers to get the sequence?

  
P1      P2
1 1     1 1      1  
1 2     1 1      2
2 1     1 2      4
2 2     1 2      8

1 1     5 3      15
1 2     5 3      30
2 1     5 5      50
2 2     5 5      100

1 1     5 7      35  
1 2     5 7      70
2 1     13 11    286
2 2     13 11    572

1 1     13 13    169
1 2     13 13    338 
2 1     13 17    442
2 2     13 17    884
.
.
.

It could be a waltz, bunny hop or something else.

Lyrics and Music

[BrainForce]

A cool sequence i made while solving max's sequence....max's ur sequence could have an aliter if 35 was 135 & 70 ..170.....

look at this sequence......

1,2,4,8,22,74,508,5552...?

 

an easy one if relate no.s sincerely...

[Qfwfq]

Now I wonder who can get this one:

 

3 3 5 4 4 3 5 5 4 3 6 6 8 8 7 7 9 9...

 

:)

[anto]

well, the answer max was awesome and it made sence, I asked my calc teacher and he said that the answer was wrong . I'll need to think a bit about Qfwfq's answer

[BrainForce]

Qfwfq ' s prob..

next in series are 8,8....i think..

[Fatstep]

75.

[BrainForce]

ya a decrease of 24 this time...i missed to count one number...

[Pyrotex]

Two years ago my Calculus teacher gave us a simple number sequence

1 2 4 8 15 30 50 100...

 

It could be an oscillating sequence function; n is the previous value:

 

1

2 = 2n

4 = 2n - 0

8 = 2n

15 = 2n - 1

30 = 2n

50 = 2n - 10

100 = 2n

100 = 2n - 100

 

hmmmm... I'm not sure that's elegant enough

[CraigD]

Two years ago my Calculus teacher gave us a simple number sequence

1 2 4 8 15 30 50 100

 

and told us to find the next term.

It could be an oscillating sequence function; n is the previous value:

 

1

2 = 2n

4 = 2n - 0

8 = 2n

15 = 2n - 1

30 = 2n

50 = 2n - 10

100 = 2n

100 = 2n - 100

 

hmmmm... I'm not sure that's elegant enough

I like that algorithm! It fits the “something a 5th grader could do” criterion, though like some of my badly not fitting-the-criterion “only tool a hammer/forward difference” solutions, plunges into the negatives in the next terms

200 = 2n

-600 = 2n -1000

 

Anto’s teacher has already said 100 is not the correct term #9, though, so that’s not it…

… 100 is not the answer b/c I've guessed 100 and he told me I was wrong. …

[anto]

yeah, pretty sure its less than 50, 100% sure its less than 100. BTW I did that exact same thing to get 100

[Qfwfq]

Qfwfq ' s prob..

next in series are 8,8....i think..

No.

 

...8 6...

[Pyrotex]

I've come up with a bizarre approach to a solution--and I'm getting close.

 

In a spreadsheet...

In the top row, starting in the 2nd column, put the primes, 5, 7, 11, 13, ....

We will call them P[n], with P[1] = 5.

In the 2nd row, starting in the 2nd column, put the sequence 1, -1, 1, -1, 1, -1, ...

We will call them our Flippers, F[n], with F[1] = 1.

 

Now below that, in the 1st column, start with the numbers 1, 2, 4, 8, 16,...

These will be our Base Numbers, B[m], each one double the one before.

 

Next to each B[m], we put the formula: A[m,n] = F[n] * Integer{ B[m]/P[n] }

 

In other words, we take our Base number, divide by the Prime in that column, and take the Integer portion only. Multiply by our Flipper, F[n] so that each subsequent A[m,n] in that row changes sign.

 

A[m,n] will be our Adjustment numbers. In each row, we will add up ALL our A[m,n] to form the Adjustment Totals, T[m].

 

At the end of each row, we take the sum: B[m] + T[m] to get our Computed Sequence, C[m]

 

We want our C[m] to be the same as the original given sequence G[m] = 1, 2, 4, 8, 15, 30, ...

 

There's no argument for ending the prime numbers at some level, so we need to represent enough primes so we can be sure the next member of C[m] is computed accurately. I go out to 59.

 

So far, I've gotten this rather bizarre sequence to agree with our G[m] up to 30; there it diverges. Needs more work.

 

Can't defend starting the Primes at 5. :eek_big:

 

Rather than use Primes, I have tried Odd numbers and am thinking of trying the Fibonacci Sequence next.

[anto]

wow..thats just amazing work O.o once you have a final answer I'll show him the work and ask if its ok, all credit goes to you of course :eek_big:

[CraigD]

I've come up with a bizarre approach to a solution--and I'm getting close.

 

In a spreadsheet...

Using about the algorithm Pyro describes, I got close to, but not quite the target sequence of 1, 2, 4, 8, 15, 30, 50, 100, ?

1=1-1/5
2=2-2/5
4=4-4/5
8=8-8/5+8/7-8/11
15=16-16/5+16/7-16/11+16/13-16/17
29=32-32/5+32/7-32/11+32/13-32/17+32/19-32/23+32/29-32/31+32/37
59=64-64/5+64/7-64/11+64/13-64/17+64/19-64/23+64/29-64/31+64/37-64/41+64/43-64/47+64/53-64/59+64/61-64/67
114=128-128/5+128/7-128/11+128/13-128/17+128/19-128/23+128/29-128/31+128/37-128/41+128/43-128/47+128/53-128/59+128/61-128/67+128/71-128/73+128/79-128/83+128/89-128/97+128/101-128/103+128/107-128/109+128/113-128/127+128/131
226=256-256/5+256/7-256/11+256/13-256/17+256/19-256/23+256/29-256/31+256/37-256/41+256/43-256/47+256/53-256/59+256/61-256/67+256/71-256/73+256/79-256/83+256/89-256/97+256/101-256/103+256/107-256/109+256/113-256/127+256/131-256/137+256/139-256/149+256/151-256/157+256/163-256/167+256/173-256/179+256/181-256/191+256/193-256/197+256/199-256/211+256/223-256/227+256/229-256/233+256/239-256/241+256/251-256/257
457=512-512/5+512/7-512/11+512/13-512/17+512/19-512/23+512/29-512/31+512/37-512/41+512/43-512/47+512/53-512/59+512/61-512/67+512/71-512/73+512/79-512/83+512/89-512/97+512/101-512/103+512/107-512/109+512/113-512/127+512/131-512/137+512/139-512/149+512/151-512/157+512/163-512/167+512/173-512/179+512/181-512/191+512/193-512/197+512/199-512/211+512/223-512/227+512/229-512/233+512/239-512/241+512/251-512/257+512/263-512/269+512/271-512/277+512/281-512/283+512/293-512/307+512/311-512/313+512/317-512/331+512/337-512/347+512/349-512/353+512/359-512/367+512/373-512/379+512/383-512/389+512/397-512/401+512/409-512/419+512/421-512/431+512/433-512/439+512/443-512/449+512/457-512/461+512/463-512/467+512/479-512/487+512/491-512/499+512/503-512/509+512/521
918=1024-1024/5+1024/7-1024/11+1024/13-1024/17+1024/19-1024/23+1024/29-1024/31+1024/37-1024/41+1024/43-1024/47+1024/53-1024/59+1024/61-1024/67+1024/71-1024/73+1024/79-1024/83+1024/89-1024/97+1024/101-1024/103+1024/107-1024/109+1024/113-1024/127+1024/131-1024/137+1024/139-1024/149+1024/151-1024/157+1024/163-1024/167+1024/173-1024/179+1024/181-1024/191+1024/193-1024/197+1024/199-1024/211+1024/223-1024/227+1024/229-1024/233+1024/239-1024/241+1024/251-1024/257+1024/263-1024/269+1024/271-1024/277+1024/281-1024/283+1024/293-1024/307+1024/311-1024/313+1024/317-1024/331+1024/337-1024/347+1024/349-1024/353+1024/359-1024/367+1024/373-1024/379+1024/383-1024/389+1024/397-1024/401+1024/409-1024/419+1024/421-1024/431+1024/433-1024/439+1024/443-1024/449+1024/457-1024/461+1024/463-1024/467+1024/479-1024/487+1024/491-1024/499+1024/503-1024/509+1024/521-1024/523+1024/541-1024/547+1024/557-1024/563+1024/569-1024/571+1024/577-1024/587+1024/593-1024/599+1024/601-1024/607+1024/613-1024/617+1024/619-1024/631+1024/641-1024/643+1024/647-1024/653+1024/659-1024/661+1024/673-1024/677+1024/683-1024/691+1024/701-1024/709+1024/719-1024/727+1024/733-1024/739+1024/743-1024/751+1024/757-1024/761+1024/769-1024/773+1024/787-1024/797+1024/809-1024/811+1024/821-1024/823+1024/827-1024/829+1024/839-1024/853+1024/857-1024/859+1024/863-1024/877+1024/881-1024/883+1024/887-1024/907+1024/911-1024/919+1024/929-1024/937+1024/941-1024/947+1024/953-1024/967+1024/971-1024/977+1024/983-1024/991+1024/997-1024/1009+1024/1013-1024/1019+1024/1021-1024/1031
1836=2048-2048/5+2048/7-2048/11+2048/13-2048/17+2048/19-2048/23+2048/29-2048/31+2048/37-2048/41+2048/43-2048/47+2048/53-2048/59+2048/61-2048/67+2048/71-2048/73+2048/79-2048/83+2048/89-2048/97+2048/101-2048/103+2048/107-2048/109+2048/113-2048/127+2048/131-2048/137+2048/139-2048/149+2048/151-2048/157+2048/163-2048/167+2048/173-2048/179+2048/181-2048/191+2048/193-2048/197+2048/199-2048/211+2048/223-2048/227+2048/229-2048/233+2048/239-2048/241+2048/251-2048/257+2048/263-2048/269+2048/271-2048/277+2048/281-2048/283+2048/293-2048/307+2048/311-2048/313+2048/317-2048/331+2048/337-2048/347+2048/349-2048/353+2048/359-2048/367+2048/373-2048/379+2048/383-2048/389+2048/397-2048/401+2048/409-2048/419+2048/421-2048/431+2048/433-2048/439+2048/443-2048/449+2048/457-2048/461+2048/463-2048/467+2048/479-2048/487+2048/491-2048/499+2048/503-2048/509+2048/521-2048/523+2048/541-2048/547+2048/557-2048/563+2048/569-2048/571+2048/577-2048/587+2048/593-2048/599+2048/601-2048/607+2048/613-2048/617+2048/619-2048/631+2048/641-2048/643+2048/647-2048/653+2048/659-2048/661+2048/673-2048/677+2048/683-2048/691+2048/701-2048/709+2048/719-2048/727+2048/733-2048/739+2048/743-2048/751+2048/757-2048/761+2048/769-2048/773+2048/787-2048/797+2048/809-2048/811+2048/821-2048/823+2048/827-2048/829+2048/839-2048/853+2048/857-2048/859+2048/863-2048/877+2048/881-2048/883+2048/887-2048/907+2048/911-2048/919+2048/929-2048/937+2048/941-2048/947+2048/953-2048/967+2048/971-2048/977+2048/983-2048/991+2048/997-2048/1009+2048/1013-2048/1019+2048/1021-2048/1031+2048/1033-2048/1039+2048/1049-2048/1051+2048/1061-2048/1063+2048/1069-2048/1087+2048/1091-2048/1093+2048/1097-2048/1103+2048/1109-2048/1117+2048/1123-2048/1129+2048/1151-2048/1153+2048/1163-2048/1171+2048/1181-2048/1187+2048/1193-2048/1201+2048/1213-2048/1217+2048/1223-2048/1229+2048/1231-2048/1237+2048/1249-2048/1259+2048/1277-2048/1279+2048/1283-2048/1289+2048/1291-2048/1297+2048/1301-2048/1303+2048/1307-2048/1319+2048/1321-2048/1327+2048/1361-2048/1367+2048/1373-2048/1381+2048/1399-2048/1409+2048/1423-2048/1427+2048/1429-2048/1433+2048/1439-2048/1447+2048/1451-2048/1453+2048/1459-2048/1471+2048/1481-2048/1483+2048/1487-2048/1489+2048/1493-2048/1499+2048/1511-2048/1523+2048/1531-2048/1543+2048/1549-2048/1553+2048/1559-2048/1567+2048/1571-2048/1579+2048/1583-2048/1597+2048/1601-2048/1607+2048/1609-2048/1613+2048/1619-2048/1621+2048/1627-2048/1637+2048/1657-2048/1663+2048/1667-2048/1669+2048/1693-2048/1697+2048/1699-2048/1709+2048/1721-2048/1723+2048/1733-2048/1741+2048/1747-2048/1753+2048/1759-2048/1777+2048/1783-2048/1787+2048/1789-2048/1801+2048/1811-2048/1823+2048/1831-2048/1847+2048/1861-2048/1867+2048/1871-2048/1873+2048/1877-2048/1879+2048/1889-2048/1901+2048/1907-2048/1913+2048/1931-2048/1933+2048/1949-2048/1951+2048/1973-2048/1979+2048/1987-2048/1993+2048/1997-2048/1999+2048/2003-2048/2011+2048/2017-2048/2027+2048/2029-2048/2039+2048/2053
…

The approach seems promising, but will need to use different, and possibly more, sequences, I think.

 

Still, I don’t think this is what the target sequences inventor intends – it doesn’t quite seem to satisfy the “any 5th grader could do it” criterion.

 

PS: this (x X1) is the MUMPS program that produced the above:

s B=1 f M=1:1 s T=B,WF=0 x X2 w !,T,"=",B s WF=1 x X2 r R s B=2*B ;X1
k P x X3,X3 s F=-1 f  x X3 s A=BP*F w:WF $s(F<1:"-",1:"+"),B,"/",P q:'A  s F=-F,T=A+T ;X2
f P=$g(P,1)+1:1 x X4 i 'Q s P(P)="" q  ;X3
s Q=0 f  s Q=$o(P(Q)) q:'Q  q:'(P#Q)  ;X4

[max4236]

Is the next number 98? Or is it smaller than that? :xparty: