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This is my seventh (and probably last) batch of sequence puzzles that are nasty and hard to solve; I stress that each of them has a clear and justifiable solution.

Sequence 1:
RC, NU, RT, RS, PI, ??, AN, PT

Sequence 2:
A, ?, D, ?, G, H, J, K, L

Sequence 3:
?, ?, ?, 1, 7, 0, 7, 1, 7, 3, 4, 8, 9, 3, 4, 1, 2, 4, 2, 5, 9, 1, ?, ?, ...

Sequence 4:
O, ?, ?, H, R, A, U, ?, U, E, ?, ?, ?, ...

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  • $\begingroup$ "seventh (and probably last)" - mind if I take over the sequence-puzzle franchise then? ;) $\endgroup$ – Rand al'Thor Mar 18 '15 at 20:20
  • $\begingroup$ @Martin - Thanks for all of the sequence puzzles. They seem to have been prepared with great skill to find a good balance between difficulty and solvability. $\endgroup$ – Len Mar 20 '15 at 4:02
  • $\begingroup$ @Len - Thanks!! I feel that this is a good point for stopping. The underlying ideas started to repeat. Perhaps I will have some new ideas two or three months from now. $\endgroup$ – Alexis Mar 22 '15 at 18:22
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Sequence 1:

TU

These are the third and fourth letters of each planet in the Solar System.

MERCURY, VENUS, EARTH, MARS, JUPITER, SATURN, URANUS, NEPTUNE
RC, NU, RT, RS, PI, TU, AN, PT

Sequence 2:

S, F

These are the keys on the home row of a standard QWERTY keyboard.

A, S, D, F, G, H, J, K, L

Sequence 3:

6, 0, 7, 7, 6

These are the digits in the decimal expansion of e, shifted down by 1.

e = 2.718281828459045235360287...
digits: 6, 0, 7, 1, 7, 0, 7, 1, 7, 3, 4, 8, 9, 3, 4, 1, 2, 4, 2, 5, 9, 1, 7, 6...

Sequence 4:

U, E, O, H, R, A
These are the second letters of each day of the week, cycled around.

MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY, SUNDAY
O, U, E, H, R, A, U, O, U, E, H, R, A, ...

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  • $\begingroup$ They were pretty easy. :P $\endgroup$ – Joe Z. Mar 18 '15 at 16:41
  • $\begingroup$ Impressive Joe, how can you be that smart? $\endgroup$ – leoll2 Mar 18 '15 at 16:42
  • $\begingroup$ I'm not really smart; the data used to generate the sequences this time around was much more well known than in the previous few. $\endgroup$ – Joe Z. Mar 18 '15 at 16:56
  • $\begingroup$ unbelievably fast answer! great job! $\endgroup$ – JLee Mar 18 '15 at 17:19

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