A345880 Lexicographically earliest sequence of prime terms such that the English names of the entries form the sequence A000040 (the prime numbers). See how in the Comments section.

5, 23, 22003, 5, 53, 13, 7, 7, 83, 15013, 3, 7, 29, 7, 3, 7, 19, 7, 179, 7, 11003, 7, 19, 5, 53, 2, 13, 5, 7, 7, 19, 29, 7, 3, 7, 19, 5, 7, 7, 19, 19, 2, 19, 7, 5, 7, 7, 19, 5, 17, 7, 19, 5, 409, 70001, 53, 13, 7, 7, 5, 17, 7, 19, 5, 409, 19, 2, 19, 7, 5, 53, 2, 13, 5, 409, 389, 19, 7, 5, 53, 2, 13, 5, 409, 29, 7, 3, 7

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 28 2021

Keywords

• nonn
• word

Comments

The first English names of the sequence are:

FIVE, TWENTY-THREE, TWENTY-TWO THOUSAND THREE, FIVE, FIFTY-THREE, THIRTEEN, SEVEN, SEVEN, EIGHTY-THREE, FIFTEEN THOUSAND THIRTEEN, THREE, SEVEN, TWENTY-NINE, SEVEN, THREE, SEVEN, NINETEEN, SEVEN, ONE HUNDRED SEVENTY-NINE, SEVEN, ELEVEN THOUSAND THREE, SEVEN, ...

If we now take the 5th letter of the above English sequence (T), the 23rd (W) and the 22003rd (O) we spell T.W.O. and 2 is the first term of A000040 (the prime numbers). We then take again the 5th letter of the sequence (T), the 53rd (H), the 13th (R), the 7th (E) and the 37th (E) to form T.H.R.E.E. and 3 is the next term of A000040. The letters in position 83, 15013, 3 and 7 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 7th one, E, for instance) to form a new name. The sequence A345713 forbids such repetitions.

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

Crossrefs

Cf. A131744, A345711, A345712, A345713, A345714, A345715 and A345879.