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A005589 Number of letters in the (American) English name of n, excluding spaces and hyphens.
(Formerly M2277)
62
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 that repeatedly applying the map k->A005589(k) to any starting value n always leads to 4 (cf. A016037, A133418). - Nov 27, 2007

For terms beyond a(100), it is required to make precise that this sequence uses the American English style, "one hundred one" (not "one hundred and one" as in BE), and short scale (10^9 = billion). - 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

Table of n, a(n) for n=0..83.

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 .

Index entries for sequences related to number of letters in n

EXAMPLE

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

MATHEMATICA

t={"zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten", "eleven", "twelve", "thirteen", "fourteen", "fifteen", "sixteen", "seventeen", "eighteen", "nineteen", "twenty", "twentyone", "twentytwo", "twentythree", "twentyfour", "twentyfive", "twentysix", "twentyseven", "twentyeight", "twentynine", "thirty", "thirtyone", "thirtytwo", "thirtythree", "thirtyfour", "thirtyfive", "thirtysix", "thirtyseven", "thirtyeight", "thirtynine", "forty", "fortyone", "fortytwo", "fortythree", "fortyfour", "fortyfive", "fortysix", "fortyseven", "fortyeight", "fortynine", "fifty", "fiftyone", "fiftytwo", "fiftythree", "fiftyfour", "fiftyfive", "fiftysix", "fiftyseven", "fiftyeight", "fiftynine", "sixty", "sixtyone", "sixtytwo", "sixtythree", "sixtyfour", "sixtyfive", "sixtysix", "sixtyseven", "sixtyeight", "sixtynine", "seventy", "seventyone", "seventytwo", "seventythree", "seventyfour", "seventyfive", "seventysix", "seventyseven", "seventyeight", "seventynine", "eighty", "eightyone", "eightytwo", "eightythree", "eightyfour", "eightyfive", "eightysix", "eightyseven", "eightyeight", "eightynine", "ninety", "ninetyone", "ninetytwo", "ninetythree", "ninetyfour", "ninetyfive", "ninetysix", "ninetyseven", "ninetyeight", "ninetynine", "onehundred"}

Table[ StringLength@ t[[n]], {n, 100}] (* Robert G. Wilson v, Nov 04 2007 *)

PROG

(PARI) A005589(n, t=[10^9, #"billion", 10^6, #"million", 1000, #"thousand", 100, #"hundred"])={ n>99 && forstep( i=1, #t, 2, n<t[i] && next; n=divrem(n, t[i]); n[1]>999 && 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

CROSSREFS

Cf. A006944 (ordinals), A052360, A052362-A052363, A134629, A133418, A016037.

Sequence in context: A011762 A195780 A063571 * A052360 A154913 A154915

Adjacent sequences:  A005586 A005587 A005588 * A005590 A005591 A005592

KEYWORD

nonn,word,nice,easy

AUTHOR

N. J. A. Sloane.

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

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Last modified October 24 08:42 EDT 2014. Contains 248516 sequences.