A075774 -id:A075774 - cp's OEIS frontend

A271108 a(n) is the number of syllables pronounced in reading the sequence up to a(n-1) in American English.

0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 14, 16, 18, 20, 22, 25, 28, 31, 34, 37, 41, 44, 47, 51, 54, 57, 61, 64, 67, 71, 75, 79, 83, 86, 89, 92, 95, 98, 101, 105, 109, 113, 118, 123, 129, 135, 141, 147, 154, 160, 165, 171, 178, 185, 191, 197, 204, 208, 212, 216, 221, 227

Offset: 0

Cody M. Haderlie, Mar 30 2016

For terms a(n>100), the American English pronunciation of the terms are used; e.g., "four hundred fifty", not "four hundred and fifty"; for terms a(n>999999999), short scale is used.

Wikipedia, Long and short scales

Cf. A075774.

# uses function in A075774
from itertools import islice
def agen(): # generator of terms
    an = 0
    while True:
        yield an
        an += A075774(an)
print(list(islice(agen(), 62))) # Michael S. Branicky, May 27 2024

a(0) = 0, a(n) = a(n-1) + S(n), where S(n) is the number of syllables in n.

a(n) = a(n-1) + A075774(n).

More terms from Michael S. Branicky, May 27 2024

A276765 Number of digits in n equals number of syllables in English name of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 13, 14, 15, 16, 18, 19, 20, 30, 40, 50, 60, 80, 90, 100, 200, 300, 400, 500, 600, 800, 900, 7000, 70000, 700000, 800001, 800002, 800003, 800004, 800005, 800006, 800008, 800009, 800010, 800012, 801000, 802000, 803000, 804000, 805000

Offset: 1

Tyler Skywalker, Sep 17 2016

Numbers n such that A055642(n) = A075774(n). - Felix Fröhlich, Sep 30 2016

			From _Felix Fröhlich_, Sep 30 2016: (Start)
13 is a term, since the decimal expansion is two digits long and "thir-teen" has two syllables.
17 is not a term, since the decimal expansion is two digits long, but "se-ven-teen" has three syllables.
800001 is a term, since the decimal expansion is six digits long and "eight -hun-dred-thou-sand-one" has six syllables. (End)

Cf. A055642, A075774.

Edited and more terms from Felix Fröhlich, Sep 30 2016

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

Original entry on oeis.org

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

Jack Zilinskas, Jun 26 2021

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

			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)

Cf. A075774.

\\ 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

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

cp's OEIS Frontend

A271108 a(n) is the number of syllables pronounced in reading the sequence up to a(n-1) in American English.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Python

Formula

Extensions

A276765 Number of digits in n equals number of syllables in English name of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Python