A345711 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 (see the Comments section).

5, 10, 20, 8, 100, 4, 7, 12, 13, 1, 19, 26, 18, 68, 69, 2, 71, 38, 6, 14, 11, 44, 9, 30, 17, 23, 24, 25, 32, 21, 28, 27, 15, 16, 22, 48, 29, 52, 31, 47, 59, 34, 36, 37, 63, 39, 40, 51, 67, 84, 126, 101, 128, 115, 76, 64, 43, 53, 83, 94, 33, 46, 82, 89, 169, 109, 93, 45, 56, 129, 99, 108, 49, 70

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 24 2021

Keywords

• nonn
• word

Comments

The first English names of the sequence are:

FIVE, TEN, TWENTY, EIGHT, ONE HUNDRED, FOUR, SEVEN, TWELVE, THIRTEEN, ONE, NINETEEN, TWENTY-SIX, EIGHTEEN, SIXTY-EIGHT, SIXTY-NINE, TWO, SEVENTY-ONE, THIRTY-EIGHT, SIX, FOURTEEN, ELEVEN, FORTY-FOUR, NINE, THIRTY, SEVENTEEN, TWENTY-THREE, TWENTY-FOUR, TWENTY-FIVE, THIRTY-TWO, TWENTY-ONE, TWENTY-EIGHT...

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 the 8th letter of the sequence (T), the 100th (W), the 4th (E), the 7th (N), the 12th (T), the 13th (Y) to form T.W.E.N.T.Y. and 20 is the double of a(2) = 10. Etc.

Crossrefs

Cf. A131744, A345712 (French version).