Numerical Sequence Puzzles

4) 0, 1, 8, 10, 16, 19, 2A
    0, 1, 8, 10, 16, 19, 24

0 + 1 = 1
1 + 7 = 8
8 + 2 = 10
10 + 6 = 16
16 + 3 = 19
19 + 5 = 24

or 1, 2, 3, ... and 7, 6, 5, ... are added interchangeably

One possible interpretation of 4) is

4) 0, 1, 8, 10, 16, 19, 2A
    0, 1, 8, 10, 16, 19, 24

1 = prev + 1
8 = prev + 7
10 = prev + 2
16 = prev + 6
19 = prev + 3
24 = prev + 5

Of course, you can look at it as two interlocking series

0, 8, 16, 24 and 1, 10, 19

Oops, I was a little later typing that up. Sorry

7) 14, 23, 28, 33, 42, 51, J9
    14, 23, 28, 33, 42, 51, 56

14 = 2 * 7
23 = 3 * 7 + 2
28 = 4 * 7
33 = 5 * 7 - 2
42 = 6 * 7
51 = 7 * 7 + 2
56 = 8 * 7

I realise that you typed J9 instead of J6 ... but I'm posting this in case that was a typo ...

6) 1, 2, 6, 21, 88, 4G5, B676
    1, 2, 6, 21, 88, 445, 2676

(1 + 1) * 1 = 2
(2 + 1) * 2 = 6
(6 + 1) * 3 = 21
(21 + 1) * 4 = 88
(88 + 1) * 5 = 445
(445 + 1) * 6 = 2676

8) 1, 18, 31, 46, 61, 88, 11I
    1, 18, 31, 46, 61, 88, 111

1 + 17 = 18
18 + 13 = 31
31 + 15 = 46
46 + 15 = 61
61 + 27 = 88
88 + 23 = 111

Not very convincing, I agree ... still looking :)

Infinity08:

# 8 IS CORRECT

SORRY, i MEANT #6 was correct - not 8

1, 2, 6, 21, 88, 445, 2676

>> SORRY, i MEANT #6 was correct - not 8

And the others ?

8, 14, 23, 28, 33, 42, 51, 59
 numbered stops for the #6 train.
      
NYC Transit, NYC Subway Map, 2005.

#4 is correct

I think #3 might be right (correct) as well....  but the others...no

imo my solution to #3 is too much of a coincidence if it's not correct ...

in #7 : so J9 was not a typo ?

And yes, I'm not convinced about my #8 solution either ...


I'll have to continue tomorrow - need some sleep now :)

http://www.mta.info/nyct/service/sixline.htm

Are A and G the same?

Just to formalize the solutions I already posted :

3) 100, 99, 92, 73, 36, -25, -1E6
    100, 99, 92, 73, 36, -25, -116

with :

      x(0) = 100
      x(i) = x(i-1) - 1 - 6 * [ Sum(k = 0 .. i-1)  k ]

for i >= 1


4) 0, 1, 8, 10, 16, 19, 2A
    0, 1, 8, 10, 16, 19, 24

with :

      x(0) = 0
      x(1) = 1
      x(2i) = x(2(i - 1)) + 8
      x(2i + 1) = x(2(i - 1) + 1) + 9

for i >= 1


7) 14, 23, 28, 33, 42, 51, J9
    14, 23, 28, 33, 42, 51, 56

with :

      x(2i) = (2i + 2) * 7
      x(4i + 1) = (4i + 1 + 2) * 7 + 2
      x(4i + 3) = (4i + 3 + 2) * 7 - 2

for i >= 0

assuming that J9 was a typo ...


6) 1, 2, 6, 21, 88, 4G5, B676
    1, 2, 6, 21, 88, 445, 2676

with :

      x(0) = 1
      x(i) = (x(i - 1) + 1) * i

for i >= 1

>> 8, 14, 23, 28, 33, 42, 51, 59
>>  numbered stops for the #6 train.

If that's true, then that's VERY obscure lol. Nothing to do with number theory :)

I never said they had anything to do with number theory...<SMILE> ...just numerical sequences
Good Job Infinity08!


Thanks

AXY