A350218 a(1) = 1. a(n) is the smallest unlisted number, the name of which does not contain the first letter of the name of a(n-1) in US English.
1, 3, 4, 2, 5, 6, 8, 30, 7, 9, 12, 11, 32, 100, 10, 101, 13, 104, 15, 16, 14, 17, 18, 34, 105, 19, 33, 106, 20, 107, 23, 109, 25, 111, 26, 400, 21, 401, 22, 404, 27, 405, 28, 406, 29, 407, 31, 409, 36, 411, 37, 500, 38, 501, 39, 504, 60, 24, 505, 61, 35, 506, 62, 40, 63, 41, 66, 42, 67, 43
Offset: 1
Programs
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Mathematica
name[n_]:=IntegerName[n,"Words"]; a[1]=1; a[n_]:=a[n]=Module[{i=1}, While[ Or[ MemberQ[Table[a[k],{k,1,n-1}],i], StringContainsQ[name[i],StringTake[name[a[n-1]],1]]], i++ ]; i]; a/@Range[70] -
Python
from num2words import num2words def n2w(n): return num2words(n).replace(" and", "") def aupton(terms): alst, aset = [1], {1} for n in range(2, terms+1): an = 1 avoid = n2w(alst[-1])[0] while an in aset or avoid in n2w(an): an += 1 alst.append(an); aset.add(an) return alst print(aupton(70)) # Michael S. Branicky, Dec 20 2021