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What are the next few numbers in each of these integer sequences? Each of them has a clear and justifiable solution.

1, 2, 3, 5, 8, 9, 12, 20, 21, 22, ??, ??, ...

50, 49, 48, 46, 45, 44, 43, 38, ..., 25, 24, 23, ??, ??, ...

11, 12, 20, 30, 80, 90, 10000, ????

... 4, 5, 6, 8, 10, 40, 46, 60, 61, ??, ??, ...

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    $\begingroup$ Hint: Although all of these are number sequences, none of them have anything to do with the actual numerical properties of the numbers themselves whatsoever. $\endgroup$
    – user88
    Apr 6 '15 at 9:33
  • $\begingroup$ ,..., means that all numbers in the interval are included? $\endgroup$
    – leoll2
    Apr 6 '15 at 10:44
  • $\begingroup$ No, it means that the numbers in the sequence between 38 and 25 were omitted, and you need to find the numbers that come after 23. $\endgroup$
    – user88
    Apr 6 '15 at 10:45
  • $\begingroup$ Any hint for the 2nd sequence? $\endgroup$
    – leoll2
    Apr 12 '15 at 9:14
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Partial answer

1)

23,25

Ordinal numbers that aren't made juxtaposing the cardinal and "-th" suffix.
Credit of this answer to Xyuzhg

3)

Googol

Numbers that when written have exactly 6 letters. 10000=myriad.

4)

64, 80

Nonnegative integers that when written out in full in English have no repeated letter.

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    $\begingroup$ Your answer for sequence 4 is correct. $\endgroup$
    – user88
    Apr 6 '15 at 9:43
  • $\begingroup$ @JoeZ. I added a solution for sequence 3. If wrong i'll delete it $\endgroup$
    – leoll2
    Apr 6 '15 at 10:29
  • $\begingroup$ The rule is correct, but you haven't given me the next number. $\endgroup$
    – user88
    Apr 6 '15 at 10:29
  • $\begingroup$ Googol is too big or ok? $\endgroup$
    – leoll2
    Apr 6 '15 at 10:37
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    $\begingroup$ Googol is the correct answer. Good job. $\endgroup$
    – user88
    Apr 6 '15 at 10:38
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Sequence 1:

23, 25 (twenty-third, twenty-fifth)

Reason:

Numbers that when written in the chronological ordinal series (first, second, third, etc.) are not the number appended with "th". ("Eighth" is "eight" + "h".)

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  • $\begingroup$ Our solutions for 1 agree everywhere.. but yours is simpler. $\endgroup$
    – Ben Frankel
    Apr 6 '15 at 12:22
  • $\begingroup$ Funny - 0 would be accepted by yours, but not mine. I suppose there are linguistic connections to be made here? $\endgroup$
    – Xyuzhg
    Apr 6 '15 at 12:31
  • $\begingroup$ Well, it's not surprising that 'th' isn't added in bare to a number ending in 't' or 'y'; "two" is 1 of 2 numbers ending in 'o' and by coincidence it becomes "second"; and I guess that the disappearing 'e' makes some sense. Somehow 'dth', 'nth', 'rth', 'xth' are all natural and easy to pronounce. The other number ending in 'o', "zero", happens to not become something special and so gets 'oth', which is also not a problem to speak. $\endgroup$
    – Ben Frankel
    Apr 6 '15 at 13:10
  • $\begingroup$ @Xyuzhg: I didn't include zero because I started counting from 1. $\endgroup$
    – user88
    Apr 6 '15 at 21:05
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The second sequence is:

21, 20

And the pattern is

the number of stars on the US flag in reverse order.

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1
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1) All numbers when written out (googol would be ten duotrigintillion) end in one of these letters: denortxy (sorted alphabetically). Take only the even spots of "denortxy" to get "eoty", and now all numbers ending in a letter from "eoty" are in our list.

..., 23, 25, 28, 29, ...

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  • $\begingroup$ Twenty ends in "y". $\endgroup$
    – user88
    Apr 6 '15 at 10:34
  • $\begingroup$ Right, aeiouy then. $\endgroup$
    – Ben Frankel
    Apr 6 '15 at 10:35
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    $\begingroup$ Also, "eight" ends in "t". $\endgroup$
    – user88
    Apr 6 '15 at 10:35
  • $\begingroup$ Oh okay nevermind then, I'll think about it. $\endgroup$
    – Ben Frankel
    Apr 6 '15 at 10:36
  • $\begingroup$ "Numbers that end in aeiouy when spelled out normally or that can end in e when spelled out how they sound" works for everything.. $\endgroup$
    – Ben Frankel
    Apr 6 '15 at 10:38
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Sequence 2:

The sequence repeats its interval at every 25
50, 49, 48, 46, 45, 44, 43, 38
25, 24, 23, 21, 20, 19, 18, 13

my closest guess anyways

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  • $\begingroup$ There are numbers between 23 and 38 in the sequence. $\endgroup$
    – user88
    Jul 14 '16 at 19:48
0
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sequence 2 29, 34 Pattern -1,-1,-2,-1,-1,-1,-5, then repeats -1,-1,+6,+5

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    $\begingroup$ Please hide your answer in spoiler tags. $\endgroup$
    – risky mysteries
    Jul 28 '20 at 0:52
  • $\begingroup$ how do i do that ? $\endgroup$
    – Kristian Forde
    Jul 31 '20 at 1:07
  • $\begingroup$ That's okay, it's one now. $\endgroup$
    – risky mysteries
    Jul 31 '20 at 12:45

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