5
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11, 12, 26, 615, 153X, ?

Just to clarify, the "X" stands for a single digit and the "?" stands for the next number in the sequence.

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3
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X=1, and the next number is 3156.

Reason:

Consider the series 1,4,9,16,25. Each number goes up by 3 then 5 then 7 then 9, and 3,5,7,9 goes up by 2 each time.

The second from the previous pair of numbers becomes the first number of the next pair of numbers following the comma. 1,1 becomes 1,2 and 1,2 becomes 2 etc.

The second number also becomes the second number of the next pair but is then modified by addition according to the series I first talked about: (1+1), (2+4), (6+9), (15+16), (16+25).

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  • $\begingroup$ Well done.... :) $\endgroup$ – Prim3numbah Nov 17 at 13:05
1
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My answer is X=4 and 5341068+5. Sketch is on photo below.

enter image description here

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  • $\begingroup$ This logic seems almost solid, but the step from 11 to 12 seems to be skipping either the "add it to itself" step, or the "add 1" step. Also, looks like you forgot to add the final +5. Upvoting anyways, since it took a really close scrutiny to find anything wrong with this answer, and if you were to replace the "double and add an increasing number" step with "add the next bigger square number", you'd have a legitimate alternate solution here, I think. $\endgroup$ – Bass Nov 17 at 15:05
  • $\begingroup$ @bass, thank you for +5 and my weak first step. $\endgroup$ – Nick Nov 18 at 0:39

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