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

1,3

Comments

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

Links

Table of n, a(n) for n=1..67.

Example

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)

Prog

(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

Crossrefs

Cf. A075774.

Sequence in context: A066236 A118203 A263465 * A064956 A348745 A110449

Adjacent sequences: A345739 A345740 A345741 * A345743 A345744 A345745

Keyword

nonn,word

Author

Jack Zilinskas, Jun 26 2021

Status

approved