editing

approved

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

"a(n) ... makes the sequence extendable" means the name of a(n) does not start with any of the letters f and s.

approved

editing

proposed

approved

editing

proposed

names = {"one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten"};

names = StringReplace[

IntegerName /@ Range[1000], {"\[Hyphen]" -> "", " " -> ""}];

lst = {1}; next[n_] := next[n] =

next[n_] := next[n] = Module[{pos = Complement[Range[Length[names]], lst], i = 1},

And[

And[ First[Characters[names[[Last[lst]]]]] != Last[Characters[names[[pos[[i]]]]]], pos[[i]] <= Length[names]],

pos[[i]] <= Length[names]

],

AppendTo[lst, pos[[i]]]

];

AppendTo[lst, pos[[i]]]]; seq[n_] := Nest[next, 1, n]; seq[365]

proposed

editing

editing

proposed

allocated for Ivan N. Ianakiev

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

1, 2, 8, 3, 28, 38, 88, 9, 10, 98, 11, 12, 108, 22, 128, 32, 138, 82, 21, 148, 92, 13, 158, 102, 122, 132, 142, 152, 162, 172, 182, 192, 202, 168, 222, 178, 232, 188, 242, 198, 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

1,2

"a(n) makes the sequence extendable" means the name of a(n) does not start with any of the letters f and s.

38 is followed by 88 as 48, 58, 68 and 78 cannot make the sequence extendable.

names = {"one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten"};

lst = {1};

next[n_] := next[n] = Module[{pos = Complement[Range[Length[names]], lst], i = 1},

While[

Or[

And[First[Characters[names[[Last[lst]]]]] != Last[Characters[names[[pos[[i]]]]]], pos[[i]] <= Length[names]],

MemberQ[{"f", "s"}, First[Characters[names[[pos[[i]]]]]]] == True

],

i++

];

AppendTo[lst, pos[[i]]]]; seq[n_] := Nest[next, 1, n]; seq[3]

Cf. A277971, A277972, A281067, A281068, A282636.

allocated

easy,nonn,word

Ivan N. Ianakiev, Feb 20 2017

approved

editing

allocated for Ivan N. Ianakiev

allocated

approved