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(While creating this sequence puzzle I checked around the site for similar content and - finding none - believe this should be its first appearance in our regular catalogue...)

In a particular sphere of knowledge†, there exists a finite sequence - governed by a simple-to-express rule - where the first ten terms are:

11, 4, 6, ?, 2, 9, 12, 1, 3, *, ...

(Here, the asterisk represents a term which cannot be defined, and the question mark conceals a value which does indeed exist but has been deliberately obfuscated as an exercise for the reader to find.)

Moreover, the final ten terms of this sequence are:

..., *, 18, 14, 22, 29, 23, 74, 54, 39, 30.

(Again, the asterisk is a placeholder for a term which cannot be defined.)

These two undefinable terms (whose positions in the sequence have a very pleasing symmetry) are distinct and the only two such members of the entire series - there exists a non-zero number of valid terms that fall between them.

TASK: Complete the sequence - what is the value of the concealed fourth term? What are the missing terms that fall between the two asterisks? (Expect to see at least one repeat value in the complete sequence...) What is the overall rule which governs the sequence?

† Yes, there are a couple of hidden clues here to help you work out which...

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The full sequence is:

11, 4, 6, 46, 2, 9, 12, 1, 3, *, 19, 3, 12, 7, 8, 15, *, 18, 14, 22, 29, 23, 74, 54, 39, 30

As the rule is

The term is from matching the letters of the alphabet to the atomic number of the first element which has the letter in its atomic symbol!

This is hinted at by 'first appearance in our regular catalogue' in the pre-text, where 'regular catalogue' is synonymous with 'periodic table'!

There is also a hint in the title, the first letters spell 'BCNOF' which is the order of elements on the second row!

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So

For reference:

enter image description here

A = Na = 11
B = Be = 4
C = C = 6
D = Pd = 46
E = He = 2
F = F = 9
G = Mg = 12
H = H = 1
I = Li = 3
J = N/A = Undefined
K = K = 19
L = Li = 3
M = Mg = 12
N = Ne = 10
O = O = 8
P = P = 15
Q = N/A = Undefined
R = Ar = 18
S = Si = 14
T = Ti = 22
U = Cu = 29
V = V = 23
W = W = 74
X = Xe = 54
Y = Y = 39
Z = Zn = 30

So to answer the questions:

- The fourth term is the element for D, which doesn't appear in any atomic symbol until the symbol for Palladium - Pd, which has atomic number 46
- The missing terms are the terms for the letters K, L, M, N, O and P, which give 19, 3, 12, 7, 8, 15
- The repeat values are 3 and 12, from Lithium - Li and Magnesium - Mg, which are the first appearances for both letters in the symbols

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  • $\begingroup$ One hidden hint (I think) is reveal spoiler the many ellipses make the question downright...well...you get the idea $\endgroup$ Commented Apr 13 at 16:43
  • $\begingroup$ This is the correct answer, of course - though '3' isn't the only repeat, note! (@n1000 Unintended, actually - just the way I write! Of the deliberate ones, there's one in the title and another in the superscript preamble.) $\endgroup$ Commented Apr 13 at 16:48
  • $\begingroup$ @Stiv corrected and got the pretext hint - but I have to admit I am clueless (no pun intended :P) for the title hint! Probably something obvious I'm missing lol but can't see it at the moment... $\endgroup$ Commented Apr 13 at 17:04
  • $\begingroup$ Indeed, and 'regular-catalogue' is reveal spoiler synonymous with 'periodic-table' . Re the title, look at the starting letter of each word... $\endgroup$ Commented Apr 13 at 17:36
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    $\begingroup$ @Stiv aha, gothca :P $\endgroup$ Commented Apr 13 at 17:48

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