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Disallowed sequences

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Disallowed sequences in the OEIS consist of or contain letters (Latin or other alphabet), non-alphanumeric symbols, and/or numbers that are not rational integers, consist of or contain subsequences (or tuples, bags, sets...) or are sequences with no first member. In 1995, Neil Sloane and Simon Plouffe gave in The Encyclopedia of Integer Sequences a small sampling of sequences disallowed in that book as Figure M4822 (1) – (12).

However, note that now that finite sequences are allowed in the OEIS, Figure M4822 (3) is now A000052, (4) is A008709, (6) is A000053, (7) is A008744, (8) is A008745, (10) is A008746.

Here is another small sampling of sequences currently disallowed in the OEIS, roughly in order from slightly likely to become allowed in the future to not likely at all.

Sequences of rational integers with digits other than 0 to 9

D000000 Numbers that are pandigital in Roman numerals, using each of the symbols I, V, X, L, C, D and M at least once. The decimal representation of this sequence (see A105417) is admissible.

{MCDXLIV, MCDXLVI, MCDXLVII, MCDXLVIII, MCDLXIV, MCDLXVI, MCDLXVII, ...}

Since digits 0 to 9 are admissible in the OEIS, one may use a base from 2 to 10, although the default is obviously base 10. The choice of another base needs to be justified (e.g. to show a digits pattern in some particular base, as in A135650 Even perfect numbers written in base 2). The hexadecimal digits A, B, C, D, E, F, are not admissible.

Sequences of numbers other than rational integers

D000001 English money in 1950.

{
1
4
,
1
4
, 1, 3, 6, 12, 24, 30, 120, 240, 1200, 2400}

Ref: EIS 1995 Fig. M4822 (1) Note that sequences of fractions are now allowed as two separate sequences (one for the numerator, one for the denominator). Even so, this particular sequence would remain somewhat awkward to include in the OEIS.

D000002 Least prime factor of
n + 0 i
. The problem of 1 is sidestepped easily enough by offsetting the sequence to start with 2. A thornier problem manifests itself with 5 and persists for many of its multiples: that its two prime factors have the same absolute value. (However, do note the presence of A062327, number of divisors of
n
over the Gaussian integers).
{None, 1 + i, 3, 1 + i, 1 + 2 i or 2 + i, 1 + i, 7, 1 + i, 3, 1 + i, 11, 1 + i, 2 + 3 i or 3 + 2 i, 1 + i, ...}
D000003
πn
. (However, look at A001672.)
{1, 3.141592654..., 9.869604401..., 31.00627668..., 97.40909103..., 306.0196848..., 961.3891936..., 3020.293228..., 9488.531016..., 29809.09933..., 93648.04748..., ...}

Sequences of letters or other symbols (including sequences that mix letters and numbers)

D000004 Letters on a QWERTY keyboard.

{Q, W, E, R, T, Y, U, I, O, P, A, S, D, F, G, H, J, K, L, Z, X, C, V, B, N, M}

D000005 Letters on a Dvorak keyboard. (Ref: M. Pastore, A+ Certification Guide, McGraw-Hill Professional (2003), p. 21.)

{P, Y, F, G, C, R, L, A, O, E, U, I, D, H, T, N, S, Q, J, K, X, B, M, W, V, Z}
D000006 First kanji radical with
n
strokes. (Ref: http://www.edrdg.org/cgi-bin/wwwjdic/wwwjdic?1R)
{一, 二, 口, 心, 玄, 瓜, 臣, 金, 面, 馬, 魚, 黍, 黽, 鼻, none, none, 龠}

D000007 Operator precedence (highest to lowest, grouped in sets of equal precedence) in C. Note that the comma is itself an operator, and so is the period. (Ref: H. Schildt, C: The Complete Reference, 3rd Ed. Osborne McGraw-Hill (1995), p. 55, Table 2-8.)

{{() [] -> .}, {! ~ ++ -- - (type) * & sizeof}, {* / %}, {+ -}, {<< >>}, {< <= > >=}, {== !=}, {&}, {^}, {|}, {&&}, {||}, {?:}, {= += -= *= /=}, {,}}

Concatenating the subsequences (or sets) which are disallowed, still leaves the disallowed sequence:

{() [] -> . ! ~ ++ -- - (type) * & sizeof * / % + - << >> < <= > >= == != & ^ | && || ?: = += -= *= /= ,}

D000008 Card ranks in solitaire.

{A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K}

D000009 Card ranks in bridge.

{2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A}

Sequences of words or phrases

D000008 The
n
th planet from the Sun at the start of the 21st century. (In 1999, Pluto was reclassified as a dwarf planet.)
{Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Pluto, Neptune}
D000009 The
n
th planet in Gustav Holst’s The Planets with addition of “Pluto” by Colin Matthews.
{Mars, Venus, Mercury, Jupiter, Saturn, Uranus, Neptune, Pluto}
D000010 Key with
n
sharps in its key signature.
{C major, G major, D major, A major, E major, B major, F-sharp major, C-sharp major}
D000011 Key with
n
flats in its key signature. (Note that
a (0)
is the same for both this sequence and the previous, and that
a (5)
of one is enharmonically equivalent with
a (7)
of the other, and that
a (6)
of both are enharmonically equivalent to each other.)
{C major, F major, B-flat major, E-flat major, A-flat major, D-flat major, G-flat major, C-flat major}
D000012 Key of Beethoven’s Symphony No.
n
. (See however A001491). For
a (10)
this assumes that Barry Cooper has correctly identified Beethoven’s sketches for his Symphony No. 10.
{C major, D major, E-flat major, B-flat major, C minor, F major, A major, F major, D minor, E-flat major}
D000013 Key of Bruckner’s Symphony No.
n
. (The offset of this sequence is actually  − 1, because the number sometimes given to Bruckner’s F minor Symphony, No. 00, is arithmetically the same as No. 0 for Bruckner’s earliest D minor Symphony.)
{F minor, D minor, C minor, C minor, D minor, E-flat major, B-flat major, A major, E major, C minor, D minor}

D000014 Santa’s reindeer in the 1823 poem “A Visit from St. Nicholas.”. (Ref: http://www.snopes.com/holidays/christmas/donner.asp)

{Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Dunder, Blixem}

D000015 Presidents and other historical figures on U.S. currency from smallest coin to largest bill prior to the State Quarters and Presidential Dollars programs.

{Lincoln, Jefferson, Roosevelt, Washington, Kennedy, Washington, Jefferson, Lincoln, Hamilton, Jackson, Franklin}

D000016 Marine Corps ribbons. Very similar to Navy ribbons. (Ref: Col. Foster & Lawrence Borts, US Military Medals: 1939 to Present 3rd Ed. Medals of America Press (1995).)

{Medal of Honor, Navy Cross, Defense Distinguished Service, Navy Distinguished Service, Silver Star, Defense Superior Service, Legion of Merit, Distinguished Flying Cross, ...}
D000017 Title of
n
th Star Trek film.
{The Motion Picture, The Wrath of Khan, The Search for Spock, The Voyage Home, The Final Frontier, The Undiscovered Country, Generations, First Contact, Insurrection, Nemesis, none}
D000018 Title of
n
th Star Wars episode.
{The Phantom Menace, Attack of the Clones, Revenge of the Sith, A New Hope, Empire Strikes Back, Return of the Jedi, The Force Awakens, The Last Jedi}

Sequences of graphically manipulated numerical symbols

D000019 The decimal digits {1, 2, 3, 4, 5, 6, 7, 8, 9, 0} with their horizontal reflections (on a vertical mirror) centered over them.
                
D000020 The decimal digits {1, 2, 3, 4, 5, 6, 7, 8, 9, 0} with their horizontal reflections (on a vertical mirror) to the right of them.

Both of these were inspired by a similar sequence in the 1995 Encyclopedia of Integer Sequences, namely M4822 (11).

Sequences of subsequences, tuples, sets, multisets (bags), ...

D000021 Numbers coprime to
n
and less than or equal to
n
.
{{1}, {1}, {1, 2}, {1, 3}, {1, 2, 3, 4}, {1, 5}, {1, 2, 3, 4, 5, 6}, {1, 3, 5, 7}, {1, 2, 4, 5, 7, 8}, {1, 3, 7, 9}, ...}

However, concatenating the above sequence of subsequences begets the allowed sequence (A038566)

{1, 1, 1, 2, 1, 3, 1, 2, 3, 4, 1, 5, 1, 2, 3, 4, 5, 6, 1, 3, 5, 7, 1, 2, 4, 5, 7, 8, 1, 3, 7, 9, ...}

Sequences of vectors, matrices or tensors

E.g. from 2 initial matrices
A1
and
A2
, define
An = An  − 2  ×  An  − 1
. (The matrix product is noncommutative, beware!)

Multidimensional sequences

For an
n
-dimensional lattice sequence we would have to create
n
sequences (one for each dimension) to include it in the OEIS.

E.g. bidimensional Sturmian sequences. (Cf. Thomas Fernique, Bidimensional Sturmian Sequences and Substitutions, 2005.)

Sequences with no first member

D000022 Left infinite sequences.

{..., -3, -2, -1, 0}

D000023 Doubly infinite sequences.

{..., -3, -2, -1, 0, 1, 2, 3, ...}

Infinite sequences with ordinality greater than ω

D000024 Odd positive integers followed by even positive integers. (A sequence with ordinality, i.e. order type, equal to
ω + ω = ω  ⋅  2   ≠   ω
.)
{1, 3, 5, 7, 9, 11, 13, 15, ..., 2, 4, 6, 8, 10, 12, 14, 16, ...}

Sequences mixing numbers and words

D000025 “FizzBuzz” game: Replace any number divisible by three with the word “Fizz,” and any number divisible by five with the word “Buzz.” But multiples of both three and five are replaced by “FizzBuzz.”

{1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz, 11, Fizz, 13, 14, FizzBuzz, 16, 17, Fizz, 19, Buzz, Fizz, 22, 23, Fizz, Buzz, 26, Fizz, 28, 29, FizzBuzz, 31, 32, Fizz, 34, Buzz, Fizz, 37, 38, Fizz, Buzz, 41, Fizz, 43, 44, FizzBuzz, 46, 47, Fizz, 49, Buzz, Fizz, 52, 53, Fizz, Buzz, 56, ...}

But see A281746.

See also