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

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, 19, 29, 10, 20, 31, 32, 33, 34, 35, 47, 12, 36, 38, 39, 41, 42, 57, 43, 44, 30, 45, 46, 77, 48, 49, 67, 51, 52, 53, 71, 54, 72, 127, 73, 55, 74, 111, 56, 75, 76, 58

Offset: 1

Author

Jack Zilinskas, Jun 26 2021

Keywords

• nonn
• word

Comments

Uses the convention of omitting a trailing 'and', so 101 is 'one hundred one' rather than 'one hundred and one.'

Examples

			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.
8, 16, and 24 all have a value per syllable of 8, so they are ordered from smallest to largest in the list.
From _Jon E. Schoenfield_, Jun 27 2021: (Start)
Table begins:
                          syllable count
   n  a(n)  name          A075774(a(n))   a(n)/A075774(a(n))
  --  ----  ------------  --------------  ------------------
   1    0   zero                 2         0/2 = 0
   2    1   one                  1         1/1 = 1
   3    2   two                  1         2/1 = 2
   4    3   three                1         3/1 = 3
   5    7   seven                2         7/2 = 3.5
   6   11   eleven               3        11/3 = 3.666666...
   7    4   four                 1         4/1 = 4
   8    5   five                 1         5/1 = 5
   9   17   seventeen            3        17/3 = 5.666666...
  10    6   six                  1         6/1 = 6
  11   13   thirteen             2        13/2 = 6.5
  12   27   twenty-seven         4        27/4 = 6.75
  13   14   fourteen             2        14/2 = 7
  14   21   twenty-one           3        21/3 = 7
  15   22   twenty-two           3        22/3 = 7.333333...
(End)
		

Crossrefs

Cf. A075774.

Programs

PARI

\\ issue: nn must be bigger than the last desired term
cmpx(x, y) = my(fx = x/A075774(x), fy = y/A075774(y)); if (fx==fy, sign(x-y), sign(fx-fy));
lista(nn) = concat(0, Vec(vecsort([1..nn], cmpx, 1))); \\ Michel Marcus, Jun 27 2021

Python

def aseq(N): return sorted(range(10*N), key=lambda x: (x/A075774(x), x))[:N]
print(aseq(67)) # Michael S. Branicky, Jun 27 2021