cp's OEIS Frontend

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.

%I A345880 #11 Nov 08 2021 04:31:50
%S A345880 5,23,22003,5,53,13,7,7,83,15013,3,7,29,7,3,7,19,7,179,7,11003,7,19,5,
%T A345880 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,
%U A345880 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
%N 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.
%C A345880 The first English names of the sequence are:
%C A345880 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, ...
%C A345880 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.
%C A345880 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.
%C A345880 No obvious pattern appears in the sequence, although the set of names is limited
%Y A345880 Cf. A131744, A345711, A345712, A345713, A345714, A345715 and A345879.
%K A345880 nonn,word
%O A345880 1,1
%A A345880 _Eric Angelini_ and _Carole Dubois_, Jun 28 2021