

A119945


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


7



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
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OFFSET

0,1


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 inline 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


REFERENCES

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


LINKS



EXAMPLE

"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.

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


PROG

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\101], 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%32t<Vecsmall(G(n)), t>64])}, [0..99]) \\ (End)


CROSSREFS



KEYWORD

nonn,easy,word


AUTHOR



EXTENSIONS



STATUS

approved



