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

1,1

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.

Links

Table of n, a(n) for n=1..74.

Crossrefs

Cf. A131744, A345712 (French version).

Sequence in context: A147390 A345715 A331142 * A300019 A115825 A115774

Adjacent sequences: A345708 A345709 A345710 * A345712 A345713 A345714

Keyword

nonn,word

Author

Eric Angelini and Carole Dubois, Jun 24 2021

Status

approved