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A350217 a(1) = 1; a(n) > a(n-1) is the smallest number whose name in English does not contain the first letter of the name of a(n-1).

%I A350217 #7 Dec 20 2021 19:14:13
%S A350217 1,3,4,6,8,30,100,300,400,600,800,2000,1000000
%N A350217 a(1) = 1; a(n) > a(n-1) is the smallest number whose name in English does not contain the first letter of the name of a(n-1).
%t A350217 name[n_]:=IntegerName[n,"Words"]; a[1]=1; a[n_]:=a[n]=Module[{i=a[n-1]+1}, While[
%t A350217 StringContainsQ[name[i],StringTake[name[a[n-1]],1]], i++ ]; i]; a/@Range[12]
%o A350217 (Python)
%o A350217 from num2words import num2words
%o A350217 def n2w(n): return num2words(n).replace(" and", "")
%o A350217 def afind(limit):
%o A350217     alst, aset = [1], {1}
%o A350217     print(1, end=", ")
%o A350217     while alst[-1] < limit:
%o A350217         an = alst[-1] + 1
%o A350217         avoid = n2w(alst[-1])[0]
%o A350217         while an in aset or avoid in n2w(an): an += 1
%o A350217         alst.append(an); aset.add(an)
%o A350217         print(an, end=", ")
%o A350217 afind(100000) # _Michael S. Branicky_, Dec 20 2021
%Y A350217 Cf. A350218, A277971, A277972.
%K A350217 nonn,word,fini,full
%O A350217 1,2
%A A350217 _Ivan N. Ianakiev_, Dec 20 2021