cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A089590 Uban numbers (the letter u is banned from the English name of the number).

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 98, 99
Offset: 1

Views

Author

Eric W. Weisstein, Nov 09 2003

Keywords

Comments

The sequence of uban numbers first differs from A052406 (the numbers not containing the digit 4) at the term 40 (forty), which is a uban number but is not 4-less.

Crossrefs

Cf. A052406.
Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A008523 (ban t).

Programs

  • Haskell
    import Data.Maybe (fromJust)
    import Data.Text (Text); import qualified Data.Text as T (all)
    import Text.Numeral.Grammar.Reified (defaultInflection)
    import qualified Text.Numeral.Language.EN as EN  -- see link
    a089590 n = a089590_list !! (n-1)
    a089590_list = filter (T.all (/= 'u') . numeral) [0..] where
       numeral :: Integer -> Text
       numeral = fromJust . EN.gb_cardinal defaultInflection
    -- Reinhard Zumkeller, Jan 23 2015
    
  • Python
    from num2words import num2words
    from itertools import islice, product
    def ok(n): return "u" not in num2words(n)
    def agen(): # generator of terms < 10**304
        base, pows = [k for k in range(1, 1000) if ok(k)], [1]
        yield from ([0] if ok(0) else []) + base
        for e in range(3, 304, 3):
            if "u" not in num2words(10**e)[4:]:
                pows = [10**e] + pows
                for t in product([0] + base, repeat=len(pows)):
                    if t[0] == 0: continue
                    yield sum(t[i]*pows[i] for i in range(len(t)))
    print(list(islice(agen(), 100))) # Michael S. Branicky, Aug 19 2022

Extensions

a(1) = 0 prepended by Reinhard Zumkeller, Jan 23 2015

A134629 Least nonnegative integer which requires n letters to spell in English, excluding spaces and hyphens. A right inverse of A005589.

Original entry on oeis.org

1, 0, 3, 11, 15, 13, 17, 24, 23, 73, 101, 104, 103, 111, 115, 113, 117, 124, 123, 173, 323, 373, 1104, 1103, 1111, 1115, 1113, 1117, 1124, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 23323, 23373, 73373, 101373, 103323, 103373, 111373, 113323, 113373, 117373, 123323, 123373
Offset: 3

Views

Author

Robert G. Wilson v, Nov 04 2007

Keywords

Comments

Variant of A080777. - R. J. Mathar, Dec 13 2008
This is one of many possible right inverses of A005589, i.e., A005589 o A134629 = id (of course on the domain of this sequence, [3 .. oo)). It does not satisfy A134629 o A005589 = id. - M. F. Hasler, Feb 25 2018

Examples

			a(3) = 1: "one", a(4) = 0: "zero", a(5) = 3: "three", a(6) = 11: "eleven", a(7) = 15: "fifteen", etc.
		

Crossrefs

Programs

Extensions

More terms and reworded name from M. F. Hasler, Feb 25 2018

A164791 a(n) is the smallest nonnegative number whose American English name has the letter "n" in the n-th position.

Original entry on oeis.org

9, 1, 9, 20, 7, 11, 15, 13, 17, 47, 27, 77, 109, 120, 107, 111, 115, 113, 117, 147, 127, 177, 327, 377, 1120, 1107, 1111, 1115, 1113, 1117, 1147, 1127, 1177, 1327, 1377, 3327, 3377, 11377, 13327, 13377, 17377, 23327, 23377, 73377, 101377, 103327, 103377
Offset: 1

Views

Author

Claudio Meller, Aug 26 2009

Keywords

Examples

			a(1)=9 ("Nine"), a(2)=1 ("oNe"), a(3)=9 ("niNe"), a(4)=20 ("tweNty").
		

References

  • GCHQ, The GCHQ Puzzle Book, Penguin, 2016. See page 70.

Crossrefs

Cf. A164789 ("o"), A164790 ("e"), A164792 ("t"), A164793 ("i"), A164794 ("f"), A164795 ("h"), A164796 ("r"), A164797 ("u").

Programs

  • Python
    from num2words import num2words
    from itertools import count, islice
    def n2w(n):
      return "".join(c for c in num2words(n).replace(" and", "") if c.isalpha())
    def a(n):
        return next(i for i in count(0) if len(w:=n2w(i))>=n and w[n-1]=="n")
    print([a(n) for n in range(1, 41)]) # Michael S. Branicky, Apr 21 2023
    
  • Python
    # faster for initial segment of sequence; uses n2w, imports above
    def agen(): # generator of terms
        adict, n = dict(), 1
        for i in count(0):
            w = n2w(i)
            if "n" in w:
                locs = [i+1 for i, c in enumerate(w) if w[i] == "n"]
                for v in locs:
                    if v not in adict: adict[v] = i
            while n in adict: yield adict[n]; n += 1
    print(list(islice(agen(), 50))) # Michael S. Branicky, Apr 21 2023

Extensions

a(25) and beyond from Michael S. Branicky, Mar 25 2021
Definition clarified by N. J. A. Sloane, Apr 20 2023. We also need a British English analog of this, just as A362121 is an analog of A164790 (a(13) will be different).

A169639 Write n in French (cf. A167507) and sum the letters using a=1, ..., z=26.

Original entry on oeis.org

64, 35, 54, 81, 82, 43, 52, 60, 58, 46, 37, 60, 71, 83, 123, 92, 64, 97, 95, 83, 72, 132, 126, 153, 154, 115, 124, 132, 130, 118, 82, 142, 136, 163, 164, 125, 134, 142, 140, 128, 97, 157, 151, 178, 179, 140, 149, 157, 155, 143, 104, 164, 158, 185, 186, 147, 156, 164
Offset: 0

Views

Author

Jacques ALARDET, Apr 04 2010

Keywords

Comments

Accents are ignored. - Chai Wah Wu, Jun 11 2021

Examples

			From _Omar E. Pol_, Jun 15 2021: (Start)
-----------------------------------------------------
   n      Name      Calculation                  a(n)
-----------------------------------------------------
   0      Zero      26 +  5 + 18 + 15           = 64
   1      Un        21 + 14                     = 35
   2      Deux       4 +  5 + 21 + 24           = 54
   3      Trois     20 + 18 + 15 +  9 + 19      = 81
   4      Quatre    17 + 21 +  1 + 20 + 18 +  5 = 82
   5      Cinq       3 +  9 + 14 + 17           = 43
   6      Six       19 +  9 + 24                = 52
   7      Sept      19 +  5 + 16 + 20           = 60
   8      Huit       8 + 21 +  9 + 20           = 58
   9      Neuf      14 +  5 + 21 +  6           = 46
  10      Dix        4 +  9 + 24                = 37
  11      Onze      15 + 14 + 26 +  5           = 60
  12      Douze      4 + 15 + 21 + 26 +  5      = 71
... (End)
		

Crossrefs

Cf. A167507, A169641 ("limit points").
For other languages see A073327 (U.S. English), A119945 (German), A161406 (Spanish).

Programs

  • PARI
    A169639(n)=vecsum([t%32|t<-Vecsmall(French(n)),t>64]) \\ Cf. A167507 for French(). - M. F. Hasler, Apr 08 2023
  • Python
    from num2words import num2words
    from unidecode import unidecode
    def A169639(n): return sum(ord(s)-96 for s in unidecode(num2words(n,lang='fr')) if s.isalpha()) # Chai Wah Wu, Jun 11 2021
    

Extensions

Edited by N. J. A. Sloane, Apr 05 2010
Offset corrected by Mohammed Yaseen, Jun 11 2021

A006944 Number of letters in the n-th ordinal number (in American English).

Original entry on oeis.org

5, 6, 5, 6, 5, 5, 7, 6, 5, 5, 8, 7, 10, 10, 9, 9, 11, 10, 10, 9, 11, 12, 11, 12, 11, 11, 13, 12, 11, 9, 11, 12, 11, 12, 11, 11, 13, 12, 11, 8, 10, 11, 10, 11, 10, 10, 12, 11, 10, 8, 10, 11, 10, 11, 10, 10, 12, 11, 10, 8, 10, 11, 10, 11, 10, 10, 12, 11, 10, 10, 12, 13, 12, 13, 12, 12
Offset: 1

Views

Author

Keywords

Comments

a(0) is ambiguous (see Wikipedia: English numerals link). It is either 6 or 7 depending on whether the word used is 'zeroth' or 'noughth'. - Jon Perry, Nov 01 2014
The ordinal numbers 101st, 102nd, etc., are commonly spoken as "one hundred and first," "one hundred and second," etc., with the word "and" following the word "hundred." The more concise wordings "one hundred first," "one hundred second," etc. (without the word "and") are recommended by numerous authoritative reference works on American English, including the AP Style Guide and the U.S. Government Printing Office Style Manual. The American convention of omitting the "and" is followed in the b-file. - Jon E. Schoenfield, Nov 04 2014

Examples

			"First" has 5 letters, so a(1)=5.
Hyphens and spaces are not counted, so, e.g., a(21)=11 ("twenty-first") and a(100)=12 ("one hundredth").
		

References

  • Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file (Science Section).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A005589.
Cf. A196278 (analog for French), A006969 (variant for French counting spaces and hyphens).

Programs

  • Python
    from num2words import num2words
    def a(n): return sum(1 for c in num2words(n, to='ordinal').replace(" and", "") if c.isalpha())
    print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Aug 08 2021 edited Jul 12 2022

Extensions

More terms from Jon E. Schoenfield, Aug 13 2007

A007005 Number of characters in the French spelling of n, including spaces and hyphens.

Original entry on oeis.org

4, 2, 4, 5, 6, 4, 3, 4, 4, 4, 3, 4, 5, 6, 8, 6, 5, 8, 8, 8, 5, 11, 10, 11, 12, 10, 9, 10, 10, 10, 6, 12, 11, 12, 13, 11, 10, 11, 11, 11, 8, 14, 13, 14, 15, 13, 12, 13, 13, 13, 9, 15, 14, 15, 16, 14, 13, 14, 14, 14, 8, 14, 13, 14, 15, 13, 12, 13, 13, 13, 12, 16, 14, 15, 17, 15, 14
Offset: 0

Views

Author

Keywords

Comments

This sequence gives the number of characters, including spaces and hyphens, in the French spelling of the numbers; e.g., a(21) = 11 = #"vingt et un", a(22) = 10 = #"vingt-deux". - M. F. Hasler, Nov 18 2009
See A167507 for a variant where only letters are counted, but spaces and hyphens are not counted. - M. F. Hasler, Jun 03 2012
See A052360 for the English version (and A005589 for the letters-only variant); A007208 for the German version. - M. F. Hasler, Sep 20 2014
This refers to the official French spelling, Swiss or Belgian variants ("septante", ...) are not considered here. - M. F. Hasler, Sep 21 2014

Examples

			a(0) = 4 = #"zéro"
a(80) = 13 = #"quatre-vingts"
a(999) = 31 = #"neuf cent quatre-vingt-dix-neuf"
a(1000) = 5 = # "mille"
		

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Programs

Extensions

a(71) and a(74) corrected by M. F. Hasler, Jun 03 2012
Example completed by Rémy Sigrist, Sep 09 2018

A008521 Numbers that do not contain the letter 'o'.

Original entry on oeis.org

3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, 27, 28, 29, 30, 33, 35, 36, 37, 38, 39, 50, 53, 55, 56, 57, 58, 59, 60, 63, 65, 66, 67, 68, 69, 70, 73, 75, 76, 77, 78, 79, 80, 83, 85, 86, 87, 88, 89, 90, 93, 95, 96, 97, 98, 99, 300, 303, 305, 306, 307
Offset: 1

Views

Author

Keywords

Comments

There are exactly 454 oban numbers. - Eric W. Weisstein, Nov 09 2003

Crossrefs

Cf. A006933 (ban e), A089589 (ban i), A008523 (ban t), A089590 (ban u).

Programs

  • Haskell
    import Data.Maybe (fromJust)
    import Data.Text (Text); import qualified Data.Text as T (all)
    import Text.Numeral.Grammar.Reified (defaultInflection)
    import qualified Text.Numeral.Language.EN as EN  -- see link
    a008521 n = a008521_list !! (n-1)
    a008521_list = filter (T.all (/= 'o') . numeral) [0..] where
       numeral :: Integer -> Text
       numeral = fromJust . EN.gb_cardinal defaultInflection
    -- Reinhard Zumkeller, Jan 23 2015
    
  • Python
    from num2words import num2words
    afull = [k for k in range(1000) if "o" not in num2words(k)]
    print(afull[:70]) # Michael S. Branicky, Aug 18 2022

A008523 Numbers that do not contain the letter 't'.

Original entry on oeis.org

0, 1, 4, 5, 6, 7, 9, 11, 100, 101, 104, 105, 106, 107, 109, 111, 400, 401, 404, 405, 406, 407, 409, 411, 500, 501, 504, 505, 506, 507, 509, 511, 600, 601, 604, 605, 606, 607, 609, 611, 700, 701, 704, 705, 706, 707, 709, 711, 900, 901, 904, 905, 906, 907, 909, 911, 1000000, 1000001, 1000004, 1000005
Offset: 1

Views

Author

Keywords

Comments

See also A006933, the eban numbers (numbers not containing 'e'), and A089589 (the iban numbers). This sequence might correspondingly be called the "tban" numbers. - WG Zeist, Aug 31 2012

Crossrefs

Cf. A006933 (ban e), A089589 (ban i), A008521 (ban o), A089590 (ban u).
Complement of A008522.

Programs

  • Haskell
    -- import Data.Maybe (fromJust)
    import Data.Text (Text); import qualified Data.Text as T (all)
    import Text.Numeral.Grammar.Reified (defaultInflection)
    import qualified Text.Numeral.Language.EN as EN  -- see link
    a008523 n = a008523_list !! (n-1)
    a008523_list = filter (T.all (/= 't') . numeral) [0..] where
       numeral :: Integer -> Text
       numeral = fromJust . EN.gb_cardinal defaultInflection
    -- Reinhard Zumkeller, Jan 23 2015
    
  • Python
    from num2words import num2words
    from itertools import islice, product
    def ok(n): return "t" not in num2words(n)
    def agen(): # generator of terms < 10**304
        base, pows = [k for k in range(1, 1000) if ok(k)], [1]
        yield from ([0] if ok(0) else []) + base
        for e in range(3, 304, 3):
            if "u" not in num2words(10**e)[4:]:
                pows = [10**e] + pows
                for t in product([0] + base, repeat=len(pows)):
                    if t[0] == 0: continue
                    yield sum(t[i]*pows[i] for i in range(len(t)))
    print(list(islice(agen(), 60))) # Michael S. Branicky, Aug 19 2022

Extensions

a(57)-a(60) from WG Zeist, Aug 31 2012

A052362 Indices of records in length of English name of n including spaces and dashes (A052360): n such that k < n => A052360(k) < A052360(n).

Original entry on oeis.org

0, 3, 11, 13, 17, 21, 23, 73, 101, 103, 111, 113, 117, 121, 123, 173, 323, 373, 1101, 1103, 1111, 1113, 1117, 1121, 1123, 1173, 1323, 1373, 3323, 3373, 11373, 13323, 13373, 17373, 21373, 23323, 23373, 73373, 101323, 101373, 103323, 103373, 111373, 113323, 113373, 117373
Offset: 1

Views

Author

Allan C. Wechsler, Mar 07 2000

Keywords

Comments

From M. F. Hasler, Aug 12 2020: (Start)
This sequence uses A052360 which counts all characters in the English name of the numbers, including spaces and hyphens, in contrast to A052363 which uses A005589 which only counts the letters. Thus, e.g., "twenty-one" is in this sequence but not in A052363.
It appears that from 1323 on, all terms end in -323 or in -373. After 117(373) these are prefixed by 121, 123, 173, 323, 373 (thousand). Then the next terms is 1'103'323, and after 1'373'373, the next terms are > 3*10^6, then > 11*10^6, etc.
I conjecture that from 103 on all d-digit terms have a smaller (most often but not always (d-1)-digit) term as suffix, and from 173 on they also have an earlier term as prefix. (End)

Examples

			From _M. F. Hasler_, Aug 12 2020: (Start)
The first term is zero, since all other nonnegative integers (thus certainly all those with longer names) are larger than zero.
"One" and "two" are not in the sequence, since "zero" is smaller but has a longer name.
"Three" is again in the sequence since all smaller numbers (0, 1 and 2) have shorter names. And so on. (End)
		

Crossrefs

Programs

  • PARI
    m=0;for(n=0,2e5, if(m<A052360(n), m=A052360(n); print1(n", "))) \\ M. F. Hasler, Aug 12 2020
    
  • Python
    from itertools import count, islice
    from num2words import num2words as n2w
    def f(n): return len(n2w(n).replace(" and", "").replace(chr(44), ""))
    def agen():
        record = 0
        for n in count(0):
            value = f(n)
            if value > record: yield n; record = value
    print(list(islice(agen(), 46))) # Michael S. Branicky, Jul 12 2022

Extensions

Minor edits by Ray Chandler, Jul 22 2009
Name and example edited and more terms by M. F. Hasler, Aug 12 2020

A073029 Names for numbers in American English, with each letter transformed into its index in the alphabet.

Original entry on oeis.org

26, 5, 18, 15, 15, 14, 5, 20, 23, 15, 20, 8, 18, 5, 5, 6, 15, 21, 18, 6, 9, 22, 5, 19, 9, 24, 19, 5, 22, 5, 14, 5, 9, 7, 8, 20, 14, 9, 14, 5, 20, 5, 14, 5, 12, 5, 22, 5, 14, 20, 23, 5, 12, 22, 5, 20, 8, 9, 18, 20, 5, 5, 14, 6, 15, 21, 18, 20, 5, 5, 14, 6, 9, 6, 20, 5, 5, 14, 19, 9, 24, 20, 5
Offset: 0

Views

Author

Zak Seidov, Aug 22 2002

Keywords

Comments

Irregular triangle read by rows, in which row n lists the successive indices of the letters in the American English name for n. For example, row one is 15, 14, 5. - N. J. A. Sloane, Apr 22 2023
Find smallest n's for which a(n)=1,2,3,4,...,26.
A: The numbers 10 and 11 never occur. The rows in which the others occur first (assuming use of the "short scale") are 1000 (thousAnd), 10^9 (Billion), 10^27 (oCtillion), 100 (hunDred), 0 (zEro), 4 (Four), 8 (eiGht), 3 (tHree), 5 (fIve), --, -- (j & k don't occur in English names of numbers), 11 (eLeven), 10^6 (Million), 1 (oNe), 0 (zerO), 10^24 (sePtillion), 10^15 (Quadrillion), 0 (zeRo), 6 (Six), 2 (Two), 4 (foUr), 5 (fiVe), 2 (tWo), 6 (siX), 20 (twentY), 0 (Zero). Converting the position in the row plus the preceding row lengths to a linear index n this yields (after subtracting 1 to match offset 0 of the sequence): 18452, ?, ?, 864, 1, 15, 33, 11, 20, -, -, 44, ?, 5, 3, ?, ?, 2, 23, 7, 17, 21, 8, 25, 115, 0. The graph nicely shows the position & frequency of the individual letters. - M. F. Hasler, Feb 06 2016

Examples

			Top row is for "zero"; "z" is the 26th letter in the alphabet, "e" the fifth, "r" the 18th and "o" the 15th, so the first row is 26,5,18,15.
		

Crossrefs

Cf. A005589 (row lengths).
Cf. A073327 (row sums).
Cf. A072922.

Programs

  • Mathematica
    alef=Characters["abcdefghijklmnopqrstuvwxyz"]; numb="zeroonetwothreefourfivesixseveneightnineteneleven[...]"; ch=Characters[numb]; seq[n_] := Position[alef, ch[[n]]][[1, 1]] (* Franklin T. Adams-Watters, Jun 02 2006 *)
    (* see the link to a001477.txt, copy the first 17 lines and then paste and assign to the variable 'str' as a string as follows *)
    str = "zeroonetwothreefourfivesixseveneightnineteneleventwelvethirteenfourteenfifteensixteen";
    Characters@ str /. Flatten[ Table[ {FromCharacterCode[96 + n] -> n}, {n, 26}]] (* Robert G. Wilson v, Jun 08 2010 *)
  • PARI
    A073029_row(n)=select(t->t>64,Vec(Vecsmall(English(n))))%32 \\ See A052360 for English(). - M. F. Hasler, Feb 06 2016
    
  • Python
    from num2words import num2words
    def row(n): return [ord(c)-96 for c in num2words(n).replace(" and", "") if c.isalpha()]
    print([e for n in range(17) for e in row(n)]) # Michael S. Branicky, Apr 22 2023

Extensions

Corrected and extended by Franklin T. Adams-Watters, Jun 02 2006, Oct 24 2006
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