A119945 - OEIS

A119945

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

%I #49 Apr 10 2023 08:42:27

%S 59,47,63,36,54,52,54,54,32,54,53,23,87,89,107,105,88,88,85,107,106,

%T 173,208,181,199,197,199,199,177,199,90,157,192,165,183,181,183,183,

%U 161,183,96,163,198,171,189,187,189,189,167,189,94,161,196,169,187,185,187,187,165

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

%C 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").

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

%C 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.

%C 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

%C 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

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

%H <a href="/index/Ge#German">Index entries for sequences related to German names of numbers</a>

%e "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.

%e 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.

%e 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.

%e From _Omar E. Pol_, Jun 15 2021: (Start)

%e -------------------------------------------------------------

%e n Name Calculation a(n)

%e -------------------------------------------------------------

%e 0 Null 14 + 21 + 12 + 12 = 59

%e 1 Eins 5 + 9 + 14 + 19 = 47

%e 2 Zwei 26 + 23 + 5 + 9 = 63

%e 3 Drei 4 + 18 + 5 + 9 = 36

%e 4 Vier 22 + 9 + 5 + 18 = 54

%e 5 Fünf --> Fuenf 6 + 21 + 5 + 14 + 6 = 52

%e 6 Sechs 19 + 5 + 3 + 8 + 19 = 54

%e 7 Sieben 19 + 9 + 5 + 2 + 5 + 14 = 54

%e 8 Acht 1 + 3 + 8 + 20 = 32

%e 9 Neun 14 + 5 + 21 + 14 = 54

%e 10 Zehn 26 + 5 + 8 + 14 = 53

%e 11 Elf 5 + 12 + 6 = 23

%e 12 Zwölf --> Zwoelf 26 + 23 + 15 + 5 + 12 + 6 = 87

%e ... (End)

%e 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

%o (PARI) From _M. F. Hasler_, Apr 08 2023: (Start)

%o 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.

%o apply( {A119945(n)=vecsum([t%32|t<-Vecsmall(G(n)),t>64])}, [0..99]) \\ (End)

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

%K nonn,easy,word

%O 0,1

%A _Wolfdieter Lang_, Jul 20 2006

%E Edited by _N. J. A. Sloane_, Jun 10 2021

%E Corrected and extended by _M. F. Hasler_, Apr 08 2023