A345713 Lexicographically earliest sequence of distinct 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, 11, 59, 3001, 7, 37, 101, 2, 41, 83, 29, 97, 3, 109, 19, 137, 223, 311, 71, 139, 31, 47, 149, 373, 13, 53, 163, 401, 67, 409, 367, 379, 197, 43, 113, 229, 257, 73, 107, 127, 151, 337, 199, 461, 499, 167, 233, 17, 503, 173, 313, 79, 331, 179, 103, 541, 577, 353, 569, 587, 227, 397, 263

Offset: 1

Author

Eric Angelini and Carole Dubois, Jun 24 2021

Keywords

• nonn
• word

Comments

The first English names of the sequence are:

FIVE, TWENTY-THREE, TWENTY-TWO THOUSAND THREE, ELEVEN, FIFTY-NINE, THREE THOUSAND ONE, SEVEN, THIRTY-SEVEN, ONE HUNDRED ONE, TWO, FORTY-ONE, EIGHTY-THREE, TWENTY-NINE, NINETY-SEVEN, THREE, ONE HUNDRED NINE, NINETEEN, ...

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 the 11th letter of the sequence (T), the 59th (H), the 3001st (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 101, 2, 41 and 83 will spell F.I.V.E. and 5 is the next term of A000040. Etc.

This sequence is the lexicographically earliest permutation of A000040 with this property.

Crossrefs

Cf. A131744, A345711, A345712, A345714, A000040.