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Nonnegative integers ordered by lowest number value per syllable (in American English) and then, in case of ties, numerically.
0

%I #41 Jul 20 2021 20:58:24

%S 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 19,29,10,20,31,32,33,34,35,47,12,36,38,39,41,42,57,43,44,30,45,46,77,

%U 48,49,67,51,52,53,71,54,72,127,73,55,74,111,56,75,76,58

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

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

%e 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 8, 16, and 24 all have a value per syllable of 8, so they are ordered from smallest to largest in the list.

%e From _Jon E. Schoenfield_, Jun 27 2021: (Start)

%e Table begins:

%e syllable count

%e n a(n) name A075774(a(n)) a(n)/A075774(a(n))

%e -- ---- ------------ -------------- ------------------

%e 1 0 zero 2 0/2 = 0

%e 2 1 one 1 1/1 = 1

%e 3 2 two 1 2/1 = 2

%e 4 3 three 1 3/1 = 3

%e 5 7 seven 2 7/2 = 3.5

%e 6 11 eleven 3 11/3 = 3.666666...

%e 7 4 four 1 4/1 = 4

%e 8 5 five 1 5/1 = 5

%e 9 17 seventeen 3 17/3 = 5.666666...

%e 10 6 six 1 6/1 = 6

%e 11 13 thirteen 2 13/2 = 6.5

%e 12 27 twenty-seven 4 27/4 = 6.75

%e 13 14 fourteen 2 14/2 = 7

%e 14 21 twenty-one 3 21/3 = 7

%e 15 22 twenty-two 3 22/3 = 7.333333...

%e (End)

%o (PARI) \\ issue: nn must be bigger than the last desired term

%o cmpx(x, y) = my(fx = x/A075774(x), fy = y/A075774(y)); if (fx==fy, sign(x-y), sign(fx-fy));

%o lista(nn) = concat(0, Vec(vecsort([1..nn], cmpx, 1))); \\ _Michel Marcus_, Jun 27 2021

%o (Python)

%o def aseq(N): return sorted(range(10*N), key=lambda x: (x/A075774(x), x))[:N]

%o print(aseq(67)) # _Michael S. Branicky_, Jun 27 2021

%Y Cf. A075774.

%K nonn,word

%O 1,3

%A _Jack Zilinskas_, Jun 26 2021