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A345742 Nonnegative integers ordered by lowest number value per syllable (in American English) and then, in case of ties, numerically.

%I A345742 #41 Jul 20 2021 20:58:24
%S A345742 0,1,2,3,7,11,4,5,17,6,13,27,14,21,22,15,23,8,16,24,25,26,9,18,37,28,
%T A345742 19,29,10,20,31,32,33,34,35,47,12,36,38,39,41,42,57,43,44,30,45,46,77,
%U A345742 48,49,67,51,52,53,71,54,72,127,73,55,74,111,56,75,76,58
%N A345742 Nonnegative integers ordered by lowest number value per syllable (in American English) and then, in case of ties, numerically.
%C A345742 Uses the convention of omitting a trailing 'and', so 101 is 'one hundred one' rather than 'one hundred and one.'
%e A345742 17 has a value per syllable of 17/3 (sev-en-teen), which is more than 5's value of 5 but less than 6's value of 6.
%e A345742 8, 16, and 24 all have a value per syllable of 8, so they are ordered from smallest to largest in the list.
%e A345742 From _Jon E. Schoenfield_, Jun 27 2021: (Start)
%e A345742 Table begins:
%e A345742                           syllable count
%e A345742    n  a(n)  name          A075774(a(n))   a(n)/A075774(a(n))
%e A345742   --  ----  ------------  --------------  ------------------
%e A345742    1    0   zero                 2         0/2 = 0
%e A345742    2    1   one                  1         1/1 = 1
%e A345742    3    2   two                  1         2/1 = 2
%e A345742    4    3   three                1         3/1 = 3
%e A345742    5    7   seven                2         7/2 = 3.5
%e A345742    6   11   eleven               3        11/3 = 3.666666...
%e A345742    7    4   four                 1         4/1 = 4
%e A345742    8    5   five                 1         5/1 = 5
%e A345742    9   17   seventeen            3        17/3 = 5.666666...
%e A345742   10    6   six                  1         6/1 = 6
%e A345742   11   13   thirteen             2        13/2 = 6.5
%e A345742   12   27   twenty-seven         4        27/4 = 6.75
%e A345742   13   14   fourteen             2        14/2 = 7
%e A345742   14   21   twenty-one           3        21/3 = 7
%e A345742   15   22   twenty-two           3        22/3 = 7.333333...
%e A345742 (End)
%o A345742 (PARI) \\ issue: nn must be bigger than the last desired term
%o A345742 cmpx(x, y) = my(fx = x/A075774(x), fy = y/A075774(y)); if (fx==fy, sign(x-y), sign(fx-fy));
%o A345742 lista(nn) = concat(0, Vec(vecsort([1..nn], cmpx, 1))); \\ _Michel Marcus_, Jun 27 2021
%o A345742 (Python)
%o A345742 def aseq(N): return sorted(range(10*N), key=lambda x: (x/A075774(x), x))[:N]
%o A345742 print(aseq(67)) # _Michael S. Branicky_, Jun 27 2021
%Y A345742 Cf. A075774.
%K A345742 nonn,word
%O A345742 1,3
%A A345742 _Jack Zilinskas_, Jun 26 2021