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%I #17 Dec 23 2024 14:53:43
%S 1,6,7,9,19,900,1000,13,901,16,905,5,15,906,17,907,908,1001,600,1005,
%T 500,1006,601,605,501,606,607,909,910,911,505,506,608,1007,912,57,913,
%U 914,915,916,917,918,919,9000,300,1008,1009,9001,609,9005,508,1010,9006,610,9007
%N Ending letter of a(n) equals starting letter of a(n+1), when spelled out in German; always choose the smallest possible number not yet used and not ending the sequence.
%C German version of A227865, a variant of A230862 without monotonicity.
%C We use "tausend" rather than "eintausend", in order to allow numbers ending in "t", like "hundert" and "acht".
%H E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-November/011824.html">Re: A sequence in your style</a>, SeqFan list, Nov 01 2013
%H <a href="/index/Ge#German">OEIS Index entries for sequences related to German names of numbers</a>
%e EinS, SechS, SiebeN, NeuN, NeunzehN, NeunhunderT, TausenD, DreizehN, NeunhunderteinS, SechzehN, NeunhundertfünF, FünF, FünfzehN, NeunhundertsechS, SiebzehN, NeunhundertsiebeN, NeunhundertachT, TausendeinS, SechshunderT, TausendfünF, FünfhunderT, TausendsechS, SechshunderteinS, SechshundertfünF, FünfhunderteinS, SechshundertsechS, SechshundertsiebeN, NeunhundertneuN, NeunhundertzehN, NeunhundertelF, FünfhundertfünF, FünfhundertsechS, SechshundertachT, TausendsiebeN, NeunhundertzwölF, FünfhundertsiebeN, NeunhundertdreizehN, NeunhundertvierzehN, NeunhundertfünfzehN, NeunhundertsechzehN, NeunhundertsiebzehN, NeunhundertachtzehN, NeunhundertneunzehN, NeuntausenD, DreihunderT, TausendachT, TausendneuN, NeuntausendeinS, SechshundertneuN, NeuntausendfünF, FünfhundertachT, TausendzehN, NeuntausendsechS, SechshundertzehN, NeuntausendsiebeN, ...
%o (PARI) /* Warning: Beyond n=150, the script may yield wrong results.*/
%o {A228442(Nmax, letters=Vec("dfnst"), values=[[3, 13], [5, 15], [9, 19], [6, 7, 16, 17], [10]],counter=[-1, 0, 0, 0, -1])= my(ok(n)=setsearch(letters, Vec(n=German(n))[#n]),a,ini,i); vector(Nmax,k, a=if(k>1, if(counter[i=setsearch(letters, ini=Vec(a=German(a))[#a])]>0, until(ok(counter[i]++), counter[i]%100<20&&next; Vec(German(counter[i]+=80))[1] != ini && counter[i] = values[i][1]*1000; break); counter[i], if(-counter[i]-->#values[i], counter[i]=values[i][1]*100, values[i][-counter[i]] )),1))} /* see A007208 for German() and A227865 for spellout() if you wish to capitalize initial and final letters */
%Y Cf. A227865, A230862.
%K nonn,word,changed
%O 1,2
%A _M. F. Hasler_, Nov 02 2013