A345879 Lexicographically earliest sequence such that the English names of the entries form the sequence A000040 (the prime numbers). See how in the Comments section.

5, 12, 21, 40, 37, 39, 4, 4, 1, 2, 3, 4, 31, 4, 3, 4, 14, 4, 8, 4, 3, 4, 14, 5, 26, 2, 22, 5, 4, 4, 14, 31, 4, 3, 4, 14, 5, 4, 4, 14, 14, 2, 14, 4, 5, 4, 4, 14, 5, 6, 4, 14, 5, 16, 5, 26, 22, 4, 4, 5, 6, 4, 14, 5, 16, 14, 2, 14, 4, 5, 26, 2, 22, 5, 16, 17, 14, 4, 5, 26, 2, 22, 5, 16, 31, 4, 3, 4, 14, 1, 17, 22, 5

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 28 2021

Keywords

• nonn
• word

Comments

The first English names of the sequence are:

FIVE, TWELVE, TWENTY-ONE, FORTY, THIRTY-SEVEN, THIRTY-NINE, FOUR, FOUR, ONE, TWO, THREE, FOUR, THIRTY-ONE, FOUR, THREE, FOUR, FOURTEEN, FOUR, EIGHT, FOUR, THREE, FOUR, FOURTEEN, FIVE, TWENTY-SIX, TWO, TWENTY-TWO,...

If we now take the 5th letter of the above English sequence (T), the 12th (W) and the 21st (O) we spell T.W.O. and 2 is the first term of A000040 (the prime numbers). We then take the 40th letter of the sequence (T), the 37th (H), the 39th (R), the 4th (E) and the 4th again (E) to form T.H.R.E.E. and 3 is the next term of A000040. The letters in position 1, 2, 3 and 4 will spell F.I.V.E. and 5 is the next term of A000040. 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 A345714 forbids such repetitions.

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

Crossrefs

Cf. A131744, A345711, A345712, A345713, A345714 and A345715.