A119945 Sum of numerical values of letters in German names of the nonnegative numbers.

59, 47, 63, 36, 54, 52, 54, 54, 32, 54, 53, 23, 87, 89, 107, 105, 88, 88, 85, 107, 106, 173, 208, 181, 199, 197, 199, 199, 177, 199, 90, 157, 192, 165, 183, 181, 183, 183, 161, 183, 96, 163, 198, 171, 189, 187, 189, 189, 167, 189, 94, 161, 196, 169, 187, 185, 187, 187, 165

Offset: 0

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• easy
• word

Comments

Letters with umlauts are interpreted respectively as "ae" (which does not appear in this entry), "oe", "ue", and "sz" (sharp s) (as in the German name of 30 = "dreißig" -> "dreissig") as "ss" (not "sz").

According to the Reder reference only "zweihundertfuenf", 205 and "zweihundertsieben", 207, satisfy a(n)=n.

This sequence is ambiguous for numbers above 100 because one can use, for instance, for 101 "hundertundeins" or "hunderteins. To avoid such ambiguities one should always stick to the shorter version.

An alternate version of this sequence could ignore umlauts (i.e., take "a" for "ä" etc), or, more in-line with the German alphabet as it is usually listed in textbooks and reference works, taken as ä=27, ö=28, ü=29 (and then maybe ß=30, which could nonetheless remain considered as a ligature of "∫s"="ss"). - M. F. Hasler, Jun 23 2013

It appears that there is no canonical version of this sequence, because of the lack of agreement even on the number of letters in the German alphabet. - N. J. A. Sloane, Jun 11 2021

Examples

			"Null" for 0 in German has numerical values (a=1, b=2, ..., z=26) [14, 21, 12, 12] which sums up to a(0)=59.
The numerical values for "zweihundertfuenf" are [26, 23, 5, 9, 8, 21, 14, 4, 5, 18, 20, 6, 21, 5, 14, 6] with sum 205.
The numerical values for "zweihundertsieben" are [26, 23, 5, 9, 8, 21, 14, 4, 5, 18, 20, 19, 9, 5, 2, 5, 14] with sum 207.
From _Omar E. Pol_, Jun 15 2021: (Start)
-------------------------------------------------------------
   n     Name               Calculation                  a(n)
-------------------------------------------------------------
   0     Null               14 + 21 + 12 + 12           = 59
   1     Eins                5 +  9 + 14 + 19           = 47
   2     Zwei               26 + 23 +  5 +  9           = 63
   3     Drei                4 + 18 +  5 +  9           = 36
   4     Vier               22 +  9 +  5 + 18           = 54
   5     Fünf  --> Fuenf     6 + 21 +  5 + 14 +  6      = 52
   6     Sechs              19 +  5 +  3 +  8 + 19      = 54
   7     Sieben             19 +  9 +  5 +  2 +  5 + 14 = 54
   8     Acht                1 +  3 +  8 + 20           = 32
   9     Neun               14 +  5 + 21 + 14           = 54
  10     Zehn               26 +  5 +  8 + 14           = 53
  11     Elf                 5 + 12 +  6                = 23
  12     Zwölf --> Zwoelf   26 + 23 + 15 +  5 + 12 +  6 = 87
... (End)
a(16) = 88 because "sechzehn" => [19, 5, 3, 8, 26, 5, 8, 14] with sum 88, as for a(17) with "siebzehn" => [19, 9, 5, 2, 26, 5, 8, 14]. - _M. F. Hasler_, Apr 08 2023
		

References

• Christian Reder, Wörter und Zahlen, Springer Verlag, Komet, Wien, 2000, p. 337.

Links

• Index entries for sequences related to German names of numbers

Crossrefs

For analogs in other languages see A073327 (U.S. English), A169639 (French), A161406 (Spanish).

Programs

PARI

G(n, eins="eins")={my(s(n, p, z, e="ein")=n=divrem(n, p); if(n[2], Str(G(n[1]*p), G(n[2])), Str(G(n[1], e), z))); if(n<20, ["null", eins, "zwei", "drei", "vier", "fuenf", "sechs", "sieben", "acht", "neun", "zehn", "elf", "zwoelf", "dreizehn", "vierzehn", "fuenfzehn", "sechzehn", "siebzehn", "achtzehn", "neunzehn"][n+1], n<100 && n%10, Str(G(n%10, "ein"), "und", G(n\10*10)), n<100, ["zwanzig", "dreissig", "vierzig", "fuenfzig", "sechzig", "siebzig", "achtzig", "neunzig"][n\10-1], n<1000, s(n, 100, "hundert"), n<10^6, s(n, 1000, "tausend"), n<10^9, s(n, 10^6, if(n\10^6>1, " Millionen ", "e Million ")), n<10^12, s(n, 10^9, if(n\10^9>1, " Milliarden ", "e Milliarde ")))}
\\ extension to Billion, Billiarde, Trillion, Trilliarde, ... is obvious. See A007208 for a variant.
apply( {A119945(n)=vecsum([t%32|t<-Vecsmall(G(n)),t>64])}, [0..99])
\\ M. F. Hasler, Apr 08 2023

Extensions

Edited by N. J. A. Sloane, Jun 10 2021

Corrected and extended by M. F. Hasler, Apr 08 2023