A282636 a(1) = 1. a(n) is the smallest natural number such that a(n) > a(n-1), the name of a(n) in (American) English ends with the letter a(n-1) starts with, and a(n) makes the sequence extendable.
1, 2, 8, 9, 10, 28, 38, 88, 89, 91, 97, 107, 122, 132, 142, 152, 162, 172, 182, 192, 202, 208, 228, 238, 248, 258, 268, 278, 288, 298, 308, 328, 338, 348, 358, 368, 378, 388, 398, 808, 809, 812, 821, 823, 825, 829, 831, 833, 835, 839, 841, 843, 845, 849, 851, 853, 855, 859
Offset: 1
Examples
38 is followed by 88 as 48, 58, 68 and 78 cannot make the sequence extendable.
Programs
-
Mathematica
names = StringReplace[ IntegerName /@ Range[1000], {"\[Hyphen]" -> "", " " -> ""}]; lst = {1}; next[n_] := next[n] = Module[{pos = Last[lst] + 1}, While[ Or[ And[First[Characters[names[[Last[lst]]]]] != Last[Characters[names[[pos]]]], pos <= Length[names]], MemberQ[{"f", "s"}, First[Characters[names[[pos]]]]] == True ], pos++ ]; AppendTo[lst, pos] ]; seq[n_] := Nest[next, 1, n]; seq[57]
Comments