0,1

Standard German orthography; a letter with an umlaut or ß is counted as a single letter: e.g., 30 maps to length("dreißig") = 7.

There are ambiguities from n=100 on, since both, "hundert" and "einhundert" are equally valid and common. The same applies for 1000 with "tausend" or "eintausend". - M. F. Hasler, Nov 03 2013

In contrast to English (A005589 vs A052360) and French (A007005 vs A167507), there are no spaces or other punctuation in German names for numbers, until 10^6 = "eine Million". - M. F. Hasler, Sep 20 2014

There also appears to be an ambiguity on whether there is an 's' in the middle of 101*10^3, "(ein)hundertein(s)tausend". - M. F. Hasler, Apr 08 2023

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

Wikipedia, Deutsch/Übersicht der Zahlen.

(PARI) /* Because names with ä, ö, ü or ß can't be entered directly as a string in the GP interface, we use a separate list for the names, for efficiency and readability of the main function. Note that the default lexicographical order is that of ISO 8859-1 character codes ("z" < "ß" < "ä"). In applications where this is not suitable, the special characters below can be replaced, e.g., with "ae, oe, ue, ss" or "a, o, u, s". [M. F. Hasler, Jul 05 2024] */

{deutsch = ["eins", "zwei", "drei", "vier", Str("f"Strchr(252)"nf"), "sechs", "sieben", "acht", "neun", "zehn", "elf", Str("zw"Strchr(246)"lf"), "dreizehn", "vierzehn", Str("f"Strchr(252)"nfzehn"), "sechzehn", "siebzehn", "achtzehn", "neunzehn", "zwanzig", Str("drei"Strchr(223)"ig"), "vierzig", Str("f"Strchr(252)"nfzig"), "sechzig", "siebzig", "achtzig", "neunzig"]}

German(n, e="eins", power=0, name="")={ if(power /* internal helper function */

, n = divrem(n, power); Str(German(n[1], e) name, if(n[2], German(n[2]), ""))

, n < 20, if(n>1, deutsch[n], n, e, "null")

, n < 100, Str(if(n%10, Str(German(n%10, "ein") "und"), "") deutsch[n\10+18])

, n < 1000, German(n, "ein", 100, "hundert") \\ replace "ein" with "" to get

, n < 10^6, German(n, "ein", 1000, "tausend")\\ hundert/tausend without "ein-"

, my(t=3); while(n>=10^t, t+=3); German(n, "ein", 10^t-=3, strprintf(

if(n\10^t>1, " %sen", t%2, "e %se", "e %s") if(n%10^t, " ", ""),

Str(["M", "B", "Tr", "Quadr", "Quint", "Sext", "Sept", "Oct", "Non",

"Dez", "Undez" /* etc. */][t\6], "illi", ["on", "ard"][t%2+1])))

)} \\ updated Mar 03 2020, Apr 08 2023, Jul 05 2024

A007208 = n -> #German(n) \\ M. F. Hasler, Nov 01 2013

A007208(n) = vecsum([c>32|c<-Vecsmall(German(n))]) \\ To exclude spaces; irrelevant for n < 10^6. - M. F. Hasler, Jul 05 2024

Cf. A005589 and A052360 (English analog).

Cf. A007005 and A167507 (French analog).

Sequence in context: A105682 A049109 A035651 * A386820 A165919 A035637

Adjacent sequences: A007205 A007206 A007207 * A007209 A007210 A007211

nonn,word

Corrected by Markus Stausberg (markus(AT)polomi.de), Aug 08 2004

Initial term a(0) = 4 = #"null" added by M. F. Hasler, Nov 01 2013

approved