A345712 Lexicographically earliest sequence of distinct positive terms such that the French names of the entries form a new sequence of French names where every original entry is doubled (see the Comments section for an explanation and the Crossrefs section for the original English version).

5, 2, 8, 4, 7, 15, 12, 17, 6, 19, 18, 11, 27, 20, 9, 10, 25, 16, 13, 14, 105, 22, 30, 98, 32, 28, 40, 108, 33, 3, 57, 38, 62, 35, 26, 65, 66, 23, 24, 136, 70, 129, 48, 75, 138, 61, 47, 87, 68, 91, 31, 173, 97, 153, 77, 29, 58, 49, 60, 93, 106, 174, 96, 59, 114, 99, 54, 55, 42, 123, 128, 188, 102, 64

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 24 2021

Keywords

• nonn
• word

References

• Translated in French, the first names of the sequence are:
• CINQ, DEUX, HUIT, QUATRE, SEPT, QUINZE, DOUZE, DIX-SEPT, SIX, DIX-NEUF, DIX-HUIT, ONZE, VINGT-SEPT, VINGT, NEUF, DIX, VINGT-CINQ, SEIZE, TREIZE, QUATORZE, CENT CINQ, VINGT-DEUX, TRENTE, QUATRE-VINGT-DIX-HUIT, TRENTE-DEUX, ...
• If we now take the 5th letter of the above French sequence (D), the 2nd (I) and the 8th (X) we spell D.I.X. (TEN in French) and 10 is the double of a(1) = 5. We then take the 4th letter of the sequence (Q), the 7th (U), the 15th (A), the 12th (T), the 17th (R) and the 6th (E) to form Q.U.A.T.R.E. (FOUR in French) and 4 is the double of a(2) = 2. Etc.

Crossrefs

Cf. A131744, A345711 (English version).