A330365 Lexicographically earliest sequence of distinct terms starting with a(1) = 1 ("one") such that the letter count of a(n) + the letter count of a(n+1) = the letter count of [a(n) + a(n+1)].

1, 10, 2, 20, 3, 30, 4, 9, 5, 40, 6, 7, 50, 8, 60, 41, 72, 42, 71, 53, 61, 51, 63, 54, 59, 55, 64, 49, 65, 57, 56, 58, 67, 46, 66, 47, 100, 11, 92, 21, 200, 12, 91, 22, 95, 18, 110, 13, 210, 15, 96, 16, 90, 14, 99, 19, 94, 32, 81, 68, 85, 36, 82, 31, 93, 34, 300, 17, 400, 23, 500, 24, 600, 25, 98, 26, 700, 27, 800, 28

Offset

1,2

Links

Hans Havermann, Table of n, a(n) for n = 1..1000

Example

one + ten = eleven (6 letters on both sides of the equal sign);
ten + two = twelve (6 letters on both sides);
two + twenty = twenty-two (9 letters on both sides);
twenty + three = twenty-three (11 letters on both sides);
three + thirty = thirty-three (11 letters on both sides);
thirty + four = thirty-four (10 letters on both sides);
four + nine = thirteen (8 letters on both sides);
nine + five = thirteen (8 letters on both sides); etc.

Mathematica

len[n_]:=StringLength[StringReplace[IntegerName[n, "Words"], {" "-> "", ", "-> "", "-"-> ""}]]; a[1]=1;
a[n_]:=a[n]=Module[{m=First[Complement[Range[n], a/@Range[n-1]]]}, While[len[a[n-1]]+len[m]!=len[a[n-1]+m]||MemberQ[a/@Range[n-1], m]==True, m++]; m];
a/@Range[100] (* Ivan N. Ianakiev, Dec 14 2019 *)

Crossrefs

Cf. A213006 (positive numbers that, spelled in English, are as long as the spelling of their digits).

Sequence in context: A005483 A228276 A040099 * A173237 A319154 A086068

Adjacent sequences: A330362 A330363 A330364 * A330366 A330367 A330368

Keyword

nonn,word

Author

Eric Angelini and Hans Havermann, Dec 12 2019

Status

approved