A345715 Lexicographically earliest sequence of distinct positive terms such that the English names of the entries form a new sequence of English names where every original entry is doubled (repetitions allowed, see the Comments section).

5, 10, 20, 5, 9, 4, 7, 5, 13, 1, 23, 25, 5, 13, 5, 4, 7, 4, 2, 119, 800, 5, 4, 4, 7, 4, 2, 119, 36, 5, 1, 23, 24, 25, 5, 4, 4, 7, 5, 4, 7, 5, 9, 4, 7, 5, 13, 26, 2, 179, 5, 9, 23, 1, 23, 25, 5, 13, 26, 2, 179, 1, 2, 1, 5, 13, 5, 4, 7, 5, 9, 4, 7, 5, 13, 26, 2, 179, 5, 4, 7, 4, 2, 119, 36, 5, 1, 23, 24, 25, 5, 4, 4

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 28 2021

Keywords

• nonn
• word

Comments

The first English names of the sequence are:

FIVE, TEN, TWENTY, FIVE, NINE, FOUR, SEVEN, FIVE, THIRTEEN, ONE, TWENTY-THREE, TWENTY-FIVE, FIVE, THIRTEEN, FIVE, FOUR, SEVEN, FOUR, TWO, ONE HUNDRED NINETEEN, EIGHT HUNDRED, FIVE, FOUR, FOUR, ...

If we now take the 5th letter of the above English sequence (T), the 10th (E) and the 20th (N) we spell T.E.N. and 10 is the double of a(1) = 5. We then take again the 5th letter of the sequence (T), the 9th (W), the 4th (E), the 7th (N), the 5th again (T), the 13th (Y) to form T.W.E.N.T.Y. and 20 is the double of a(2) = 10. Etc.

We are allowed to use the same letter many times (like the 4th one, E, for instance) to form a new name. The sequence A345711 forbids such repetitions.

No obvious pattern appears in the sequence, although the set of names is limited.

Crossrefs

Cf. A131744, A345711, A345712, A345713, A345714.