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What is the next number in the sequence: 1 4 23 25 26 ?

Also, could you answer the logic that goes with it.

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The next number is:

28

Method:

I plugged the numbers into hexadecimal to text convertor and found the following sequence: #%&. I found this interesting because on my keyboard, it's the shift position for the values 3, 5, and 7 on a computer.

enter image description here

Therefore, the next logical step is Shift-9, or (. The full correct sequence is #%&(, and ( in hex is the number we need.

I think the 1 and 4 are red herrings, or just cool because today I learned about SOH and EOT.

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    $\begingroup$ You surely rock! $\endgroup$ – Nickil Maveli May 25 '16 at 21:07
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    $\begingroup$ Oh snap, my first solved puzzle! Thank you :D $\endgroup$ – Adib May 25 '16 at 21:18
  • $\begingroup$ Well this just does not work here in the U.K. as $23$ would need to be $A3$. It also wont work for standard keyboards in France, Germany, Italy, Norway, Portugal, Spain, Sweden, or Finland - not to mention any of the countries outside of Europe, some of which are quite large like China, India, Russia and Brazil. $\endgroup$ – Jonathan Allan May 26 '16 at 1:06
  • $\begingroup$ @JonathanAllan That's true. I guess the original questionnaire had to be more clear with the question. Otherwise, I guess based on what he thought was right, I solved the puzzle $\endgroup$ – Adib May 26 '16 at 1:19
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The next number is

91

Because it is

The closest integer value of the polynom. $2.04 x^4 - 25.9 x^3 + 112.4 x^2 - 183.5 x + 96$
for x=6, the previous numbers being the values from 1 to 5

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  • $\begingroup$ Wow! There must be a simpler way than that. $\endgroup$ – Nickil Maveli May 24 '16 at 18:16
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    $\begingroup$ @NickilMaveli in case you didn't realize, fffred is not really seriously suggesting this as an answer... $\endgroup$ – Memming May 24 '16 at 18:21
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    $\begingroup$ There should be a special markup for sarcasm. $\endgroup$ – Marius May 24 '16 at 18:52
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This was a trick question.

There are no other numbers in the sequence

...because

All the numbers in the sequence are the solutions to the equation $x^5-79 x^4+2197 x^3-24361 x^2+82042 x-59800 = 0$ and there are only 5 of them.

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  • $\begingroup$ Boom. Solid answer. Clearly it's the only correct answer, it should be accepted already. XD $\endgroup$ – Reti43 May 24 '16 at 23:06
  • $\begingroup$ @Reti43. You forgot to use the "sarcasm" markup in your comment. $\endgroup$ – Marius May 25 '16 at 6:25
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    $\begingroup$ @Marius I think that XD counts as <sarcasm> $\endgroup$ – bleh May 26 '16 at 1:55

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