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What is the next number in this sequence?

7, 10, 12, 19, 20, 30, _____

Note: I added another number as at first the pattern fit this too well.

Hint 1:

Try squaring the numbers

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    $\begingroup$ oeis.org/A029904 did you try oeis? $\endgroup$
    – Oray
    Oct 13, 2018 at 16:36
  • $\begingroup$ The only match in OEIS is A029904, but it begins with 0, 2, then 7, 10... $\endgroup$
    – user46002
    Oct 13, 2018 at 17:35
  • $\begingroup$ @Oray It's not oeis, its just a coincidence :P $\endgroup$ Oct 13, 2018 at 18:06

1 Answer 1

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I personally think (99.99%) this is very wrong but here goes,

(Q, W, E, R, T, and Y are all variables)

The pattern is just like the title said. The general idea is that Q x 1 + W x 2 + E x 3 + R x 4 + T x 5 + Y x 6 and so on is almost equal to a cube number

For 7

7 x 1 is very near to 8 = 2^3

For 7, 10

7 x 1 + 10 x 2 = 27 is equal to 27 = 3^3 (Don't know why. Must be a mistake?)

For 7, 10, 12

7 x 1 + 10 x 2 + 12 x 3 = 63 is almost equal to 64 = 4^3

For 7, 10, 12, 19

7 x 1 + 10 x 2 + 12 x 3 + 19 x 4 = 139 is quite near to 125 = 5^3 (A stretch, actually)

For 7, 10, 12, 19, 20

7 x 1 + 10 x 2 + 12 x 3 + 19 x 4 + 20 x 5 =239 is almost equal to 216 = 6^3 (Again, not sure about this)

However ,for 7, 10, 12, 19, 20, 30

7 x 1 + 10 x 2 + 12 x 3 + 19 x 4 + 20 x 5 + 30 x 6 = 419 while 7^3 = 343 (Quite far, actually)

Still, I am going to write an answer (A = Variable/Answer)

8^3 = 512 and 7 x 1 + 10 x 2 + 12 x 3 + 19 x 4 + 20 x 5 + 30 x 6 + A x 7 should almost be equal to 512. So, A x 7 = 93 and the nearest A (that is an integer) is 13

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  • $\begingroup$ This is creative, but this is too broad $\endgroup$ Oct 14, 2018 at 14:29
  • $\begingroup$ Don't think about the title too much $\endgroup$ Oct 14, 2018 at 14:29
  • $\begingroup$ @PotatoLatte Damn, well, back to the drawing board :D $\endgroup$
    – Kevin L
    Oct 15, 2018 at 2:34

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