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A282637 a(1) = 1. a(n) is the smallest unlisted natural number whose name in (American) English ends with the letter a(n-1) starts with, and makes the sequence extendable.

%I A282637 #8 Apr 28 2019 18:24:01
%S A282637 1,2,8,3,28,38,88,9,10,98,11,12,108,22,128,32,138,82,21,148,92,13,158,
%T A282637 102,122,132,142,152,162,172,182,192,202,168,222,178,232,188,242,198,
%U A282637 252,208,228,238,248,258,268,278,288,298,308,328,338,348,358,368,378,388,398,808,23,828,25,838,29,848
%N A282637 a(1) = 1. a(n) is the smallest unlisted natural number whose name in (American) English ends with the letter a(n-1) starts with, and makes the sequence extendable.
%C A282637 "a(n) ... makes the sequence extendable" means the name of a(n) does not start with any of the letters f and s.
%e A282637 38 is followed by 88 as 48, 58, 68 and 78 cannot make the sequence extendable.
%t A282637 names = StringReplace[
%t A282637    IntegerName /@ Range[1000], {"\[Hyphen]" -> "", " " -> ""}];
%t A282637 lst = {1}; next[n_] := next[n] =
%t A282637   Module[{pos = Complement[Range[Length[names]], lst], i = 1},
%t A282637    While[
%t A282637     Or[
%t A282637      And[
%t A282637       First[Characters[names[[Last[lst]]]]] != Last[Characters[names[[pos[[i]]]]]],
%t A282637       pos[[i]] <= Length[names]
%t A282637       ],
%t A282637      MemberQ[{"f", "s"}, First[Characters[names[[pos[[i]]]]]]] == True
%t A282637      ],
%t A282637     i++
%t A282637     ];
%t A282637    AppendTo[lst, pos[[i]]]
%t A282637    ];
%t A282637 seq[n_] := Nest[next, 1, n]; seq[65]
%Y A282637 Cf. A277971, A277972, A281067, A281068, A282636.
%K A282637 easy,nonn,word
%O A282637 1,2
%A A282637 _Ivan N. Ianakiev_, Feb 20 2017