The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005589 Number of letters in the US English name of n, excluding spaces and hyphens. (Formerly M2277) 81
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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). For terms beyond a(100), note that 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 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 Ely Golden, Table of n, a(n) for n = 0..11159 Eureka, Problems Drive, Eureka, 37 (1974), 8-11, 32-33, 24-27. (Annotated scanned copy) Mathematica Stack Exchange, How to express an integer number in English words? Landon Curt Noll, The English Name of a Number. Eric Weisstein's World of Mathematics, Number Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens. EXAMPLE Note that A052360(373373) = 64 whereas a(373373) = 56. 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 *) PROG (PARI) A005589(n, t=[10^9, #"billion", 10^6, #"million", 1000, #"thousand", 100, #"hundred"])={ n>99 && forstep( i=1, #t, 2, n999 && error("n >= ", 1000*t[1], " not yet implemented"); 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)))}  \\ M. F. Hasler, Jul 26 2011 (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 CROSSREFS Cf. A006944 (ordinals), A052360, A052362, A052363, A134629, A133418, A016037. Sequence in context: A011762 A195780 A063571 * A052360 A263046 A154913 Adjacent sequences:  A005586 A005587 A005588 * A005590 A005591 A005592 KEYWORD nonn,word,nice,easy AUTHOR 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 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 17:09 EDT 2020. Contains 337321 sequences. (Running on oeis4.)