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

1,2

Comments

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

Links

Table of n, a(n) for n=1..58.

Example

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

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]

Crossrefs

Cf. A277971, A277972, A281067, A281068, A282637.

Sequence in context: A360427 A369204 A237280 * A019511 A103190 A345019

Adjacent sequences: A282633 A282634 A282635 * A282637 A282638 A282639

Keyword

easy,nonn,word

Author

Ivan N. Ianakiev, Feb 20 2017

Status

approved