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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.

A005589 Number of letters in the US English name of n, excluding spaces and hyphens.

Original entry on oeis.org

4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, 8, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 5, 8, 8, 10, 9, 9, 8, 10, 10, 9, 5, 8, 8, 10, 9, 9, 8, 10, 10, 9, 5, 8, 8, 10, 9, 9, 8, 10, 10, 9, 7, 10, 10, 12, 11, 11, 10, 12, 12, 11, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 6, 9, 9, 11, 10, 10, 9, 11, 11, 10, 10, 13, 13, 15, 14, 14, 13, 15, 15, 14, 13, 16, 16, 18, 18, 17, 17, 19, 18, 18, 16
Offset: 0

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Author

N. J. A. Sloane

Keywords

Comments

Diane Karloff observes (Nov 27 2007) that repeatedly applying the map k->A005589(k) to any starting value n always leads to 4 (cf. A016037, A133418).
The above observation was previously made in 1972 by R. Schroeppel and R. W. Gosper in HAKMEM (Item 134). - Bartlomiej Pawlik, Jun 12 2023
For terms beyond a(100), this sequence uses the US English style, "one hundred one" (not "one hundred and one"), and the short scale (a billion = 10^9, not 10^12). - M. F. Hasler, Nov 03 2013
Explanation of Diane Karloff's observation above: In many languages there exists a number N, after which all numbers are written with fewer letters than the number itself. N is 4 in English, German and Bulgarian, and 11 in Russian. If in the interval [1,N] there are numbers equal to the number of their letters, then they are attractors. In English and German the only attractor is 4, in Bulgarian 3, in Russian there are two, 3 and 11. In the interval [1,N] there may also exist loops of numbers, for instance 4 and 6 in Bulgarian (6 and 4 letters respectively) or 4,5 and 6 in Russian (6,4 and 5 letters respectively). There are no loops in English, therefore the above observation is true. - Ivan N. Ianakiev, Sep 20 2014

Examples

			Note that A052360(373373) = 64 whereas a(373373) = 56.

References

  • Problems Drive, Eureka, 37 (1974), 8-11 and 33.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A006944 (ordinals), A052360, A052362, A052363, A134629, A133418, A016037.
See A362123 for another version.
Cf. A007208 (analog for German).

Programs

  • Mathematica
    inWords[n_] := Module[{r,
numNames = {"", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine"},
teenNames = {"ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen"},
tensNames = {"", "ten", "twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety"},
decimals = {"", "thousand", "million", "billion", "trillion", "quadrillion", "quintillion", "sextillion", "septillion", "octillion", "nonillion", "decillion", "undecillion", "duodecillion", "tredecillion", "quattuordecillion", "quindecillion", "sexdecillion", "septendecillion", "octodecillion", "novemdecillion", "vigintillion", "unvigintillion", "duovigintillion", "trevigintillion", "quattuorvigintillion", "quinvigintillion", "sexvigintillion", "septenvigintillion", "octovigintillion", "novemvigintillion", "trigintillion", "untrigintillion", "duotrigintillion"}},
r = If[# != 0, numNames[[# + 1]] <> "hundred"
(* <> If[#2 != 0||#3 != 0," and",""] *),
""] <> Switch[#2, 0, numNames[[#3 + 1]], 1, teenNames[[#3 + 1]], _, tensNames[[#2 + 1]] <> numNames[[#3 + 1]]] & @@@
(PadLeft[ FromDigits /@ Characters@ StringReverse@#, 3] & /@ StringCases[ StringReverse@ IntegerString@ n, RegularExpression["\\d{1,3}"]]);
StringJoin@ Reverse@ MapThread[ If[# != "", StringJoin[##], ""] &, {r, Take[decimals, Length@ r]} ]]; (* modified for this sequence from what is presented in the link and good to 10^102 -1 *)
f[n_] := StringLength@ inWords@ n; f[0] = 4; Array[f, 84, 0]
(* Robert G. Wilson v, Nov 04 2007 and revised Mar 31 2015, small revision by Ivan Panchenko, Nov 10 2019 *)
a[n_] := StringLength[ StringReplace[ IntegerName[n, "Words"], "," | " " | "\[Hyphen]" -> ""]]; a /@ Range[0, 83] (* Mma version >= 10, Giovanni Resta, Apr 10 2017 *)
  • PARI
    A005589(n, t=[10^12, #"trillion", 10^9, #"billion", 10^6, #"million", 1000, #"thousand", 100, #"hundred"])={ n>99 && forstep( i=1, #t, 2, n999 && error("n >= 10^",valuation(t[1],10)+3," requires extended 2nd argument"); return( A005589(n[1])+t[i+1]+if( n[2], A005589( n[2] )))); if( n<20, #(["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen"][n+1]), #([ "twenty", "thirty", "forty", "fifty", "sixty", "seventy", "eighty", "ninety" ][n\10-1])+if( n%10, A005589(n%10)))}  \\ Extension of 2nd arg to larger numbers is easy using the names listed in Mathematica section above. Only the string lengths are required, so it's easy to extend this list further without additional knowledge and without writing out the names. - M. F. Hasler, Jul 26 2011, minor edit on Jun 15 2021
  • Python
    from num2words import num2words
def a(n):
    x = num2words(n).replace(' and ', '')
    l = [chr(i) for i in range(97, 123)]
    return sum(1 for i in x if i in l)
print([a(n) for n in range(101)]) # Indranil Ghosh, Jul 05 2017

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Allan C. Wechsler, Mar 20 2000
Erroneous b-file deleted by N. J. A. Sloane, Sep 25 2008
More than the usual number of terms are shown in the DATA field to avoid confusion with A362123. - N. J. A. Sloane, Apr 20 2023

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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