A075774 -id:A075774 - cp's OEIS frontend

A002810 Smallest number containing n syllables in UK English.

1, 7, 11, 27, 77, 107, 111, 127, 177, 777, 1127, 1177, 1777, 7777, 11777, 27777, 77777, 107777, 111777, 127777, 177777, 777777, 1127777, 1177777, 1777777, 7777777, 11777777, 27777777, 77777777, 107777777, 111777777, 127777777, 177777777, 777777777

Offset: 1

N. J. A. Sloane

This sequence uses UK English as opposed to US English. a(6) = 107 since "one hundred and seven" has six syllables. - N. J. A. Sloane, Nov 24 2009
Because of this convention, we do not have A075774(a(n))=n, since A075774 uses US English, i.e., without the "trailing 'and'". All terms from a(6)=107 on will have this 'and', therefore A075774(a(n)) = n-1 for 5 < n < 18. From a(18)=107777 on, there is a second 'and', etc. See A045736 for the "American English" version, see A001167 for the analog considering the number of words. - M. F. Hasler, Nov 03 2013
From Bernard Schott, Feb 18 2019: (Start)
a(19) = 111777 is precisely the number used for Berry's paradox. In UK English the name of the number 111777 requires 19 syllables -- "one hundred and eleven thousand seven hundred and seventy-seven" -- and it's exactly the smallest number containing 19 syllables in UK English.
The paradox occurs when we consider that this integer is "the least integer not nameable in fewer than nineteen syllables" yet 111777 has just now been defined in eighteen syllables with this last sentence. So there is a contradiction, because the smallest integer expressible in no fewer than nineteen syllables can be expressed in eighteen syllables. This contradiction is Berry's paradox. (End)

			"One" has one syllable, therefore a(1)=1; a(2)=7 since "seven" is the least number to have two syllables; a(3)=11 because eleven is the first to have 3 syllables.

Rodolfo Kurchan, Mesmerizing Math Puzzles, by Sterling Publications, 2000, p. 18.
R. C. Penner, Discrete Mathematics, Proofs Techniques and Mathematical Structures, World Scientific, 1999, Reprinted 2001, p. 97.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Revised edition, 1997, p. 171.

Eric Weisstein's World of Mathematics, Berry Paradox
Wiktionary, one hundred one (US)
Wiktionary, one hundred and one (UK)
Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens.
Index to OEIS: sequences related to English words for n

Cf. A045736.

A002810(n)={if(n>12, A002810(n-4*n=(n-1)\12*3)*10^n+10^n\9*7, [1, 7, 11, 27, 77, 107, 111, 127, 177, 777, 1127, 1177][n])} \\ Valid up to a(58) (or a(84) when long scale is used). - M. F. Hasler, Nov 03 2013

a(n+12) = a(n)*1000+777, as long as a(n+12) is less than one quadrillion (whatever scale is used). - M. F. Hasler, Nov 03 2013

Edited and extended by M. F. Hasler, Nov 03 2013

A089746 Period 12: repeat (4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3). (Number of syllables in English name of the months.)

Original entry on oeis.org

4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3

Offset: 1

Drexel Hallaway (drexel(AT)cs.columbia.edu), Jan 08 2004

Original definition: Number of syllables in English name of n-th month, with comment: Period 12.

The original definition corresponds to the finite subsequence a(1)..a(12). There is no 13th month of the year. If "of the year" is omitted on purpose, there's no reason that the 1st month be January: the first day of the currently used Gregorian calendar was October 15, 1582, so the 1st month should be October. Originally the first month was March (whence the names September, ..., December for the 7th, ..., 10th month) and January was the 11th month. - M. F. Hasler, Feb 25 2018

			For example, January is pronounced with four syllables: Jan-u-ar-y.

Marilyn vos Savant (marilyn(AT)parade.com), column in Parade magazine, 2003.

Index entries for sequences related to calendars
Index entries for 12-periodic sequences
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A031189, A031139, A075774.

a(n)=digits(344121122333)[n%12+1] \\ M. F. Hasler, Feb 25 2018

G.f.: x*(-3*x^11 - 3*x^10 - 3*x^9 - 3*x^8 - 2*x^7 - 2*x^6 - x^5 - x^4 - 2*x^3 - x^2 - 4*x - 4)/(x^12 - 1). - Chai Wah Wu, Feb 16 2021

Thanks to Ray Chandler for supplying the explanation for this sequence.

Edited by M. F. Hasler, Feb 25 2018

A163648 Primes p with a prime number of syllables in their name in American English.

Original entry on oeis.org

7, 11, 13, 17, 19, 23, 29, 31, 41, 43, 53, 59, 61, 83, 89, 107, 113, 127, 137, 157, 167, 173, 179, 197, 227, 257, 271, 307, 313, 337, 347, 367, 373, 379, 397, 419, 457, 467, 479, 487, 547, 557, 571, 587, 607, 613, 619, 647, 673, 701, 709, 733, 739, 743, 751

Offset: 1

Jonathan Vos Post, Aug 02 2009

The word "and" is excluded, 101 is "one hundred one" rather than "one hundred and one."

See A231073 and A231075 for the analogs counting words resp. letters. - M. F. Hasler, Nov 03 2013

			a(1) = 7, which has a prime number, 2, of syllables sev-en. a(2) = 11, which has a prime number, 3, of syllables e-lev-en.

Index to OEIS: sequences related to English words for n

Cf. A000040, A075774, A164043.

forprime(p=1,900,isprime(A075774(p))&&print1(p",")) \\ - M. F. Hasler, Nov 03 2013

is(p)=isprime(A075774(p))&&isprime(p) \\ - M. F. Hasler, Nov 03 2013

# uses function in A075774
from sympy import isprime
def ok(n): return isprime(A075774(n)) and isprime(n)
print([k for k in range(800) if ok(k)]) # Michael S. Branicky, May 27 2024

{p in A000040 such that A075774(p) is in A000040}.

Extended and edited by Charles R Greathouse IV, Nov 02 2009

Values double-checked by M. F. Hasler, Nov 03 2013

A045736 Smallest positive integer requiring n syllables to pronounce in American English.

Original entry on oeis.org

1, 7, 11, 27, 77, 111, 127, 177, 777, 1127, 1177, 1777, 7777, 11777, 27777, 77777, 111777, 127777, 177777, 777777, 1127777, 1177777, 1777777, 7777777, 11777777, 27777777, 77777777, 111777777, 127777777, 177777777, 777777777, 1127777777, 1177777777, 1777777777

Offset: 1

Brian Galebach

Assumes the American usage of billion, trillion, etc. ("short scale"), which makes a difference from a(59) on.

See A002810 for the British English version, which in particular includes the additional "and", e.g., in "one hundred and seven". Therefore the sequences differ from a(6)=111 on, with A002810(6)= 107. - M. F. Hasler, Nov 03 2013

Robert G. Wilson v, English names for the numbers from 0 to 11159 without spaces or hyphens.
Index to OEIS: sequences related to English words for n

Cf. A002810.

A045736(n)={n>11 || for(k=1,1e5,A075774(k)==n && return(k)); A045736(n-11*n=(n-1)\11)*1000^n+1000^n\9*7 } \\ This code is valid up to n=58 (short scale) or n=82 (long scale). - M. F. Hasler, Nov 03 2013

a(n) = min{ k | A075774(k)=n }. - M. F. Hasler, Nov 03 2013

a(n+11) = a(n)*1000+777, as long as a(n+11) is less than one quadrillion (whatever scale is used). - M. F. Hasler, Nov 03 2013

A180961 Numbers such that the American English name of the number has four syllables.

Original entry on oeis.org

27, 37, 47, 57, 67, 71, 72, 73, 74, 75, 76, 78, 79, 87, 97, 101, 102, 103, 104, 105, 106, 108, 109, 110, 112, 201, 202, 203, 204, 205, 206, 208, 209, 210, 212, 301, 302, 303, 304, 305, 306, 308, 309, 310, 312, 401, 402, 403, 404, 405, 406, 408, 409, 410, 412

Offset: 1

Kyle Stern, Sep 28 2010

There are a finite number of terms, considering all terms up to 10^66 using English names of large numbers and various conventional extensions thereof (see Wikipedia link). - Michael S. Branicky, May 27 2024

			27 = "twen-ty sev-en", 101 = "one hun-dred one"

Kyle Stern, Table of n, a(n) for n = 1..100
Wikipedia, Names of Large Numbers

Cf. A075774.

# uses function in A075774
print([k for k in range(500) if A075774(k) == 4]) # Michael S. Branicky, May 27 2024

A075774(a(n)) = 4. - Michael S. Branicky, May 27 2024

Corrected by Kyle Stern, Sep 30 2010

A230956 Semiprimes k with a semiprime number of syllables in their name in American English.

Original entry on oeis.org

57, 74, 87, 106, 111, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 169, 183, 185, 194, 201, 202, 203, 205, 206, 209, 217, 221, 226, 235, 249, 253, 254, 259, 262, 265, 289, 291, 295, 298, 299, 301, 302, 303, 305, 309

Offset: 1

Jonathan Vos Post, Nov 04 2013

This is to A163648 as semiprimes A001358 are to primes A000040.
The word "and" is excluded, 101 is "one hundred one" rather than "one hundred and one."
Number of syllables in n in American English is A075774.
See A231073 and A231075 for prime analogs counting words respectively letters.

			87 is in the sequence because 87 = 3 * 29 is semiprime, "eighty-seven" has 4 syllables, and 4 = 2^2 is also semiprime.
106 is in the sequence because 106 = 2 * 53 is semiprime and "one hundred six" has semiprime 4 syllables.
111 is in the sequence because 111 = 3 * 37 is semiprime and "one hundred eleven" has semiprime 6 = 2*3 syllables.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001358, A075774, A163648, A231073, A231075.

# uses function in A075774
from sympy import factorint
def issemiprime(n): return sum(factorint(n).values()) == 2
def ok(n): return issemiprime(A075774(n)) and issemiprime(n)
print([k for k in range(310) if ok(k)]) # Michael S. Branicky, May 27 2024

{k: k is in A001358 and A075774(k) is in A001358}.

Corrected and extended by Charles R Greathouse IV, Jan 23 2014

A372807 Numbers whose American English name has exactly three syllables.

Original entry on oeis.org

11, 17, 21, 22, 23, 24, 25, 26, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 61, 62, 63, 64, 65, 66, 68, 69, 70, 81, 82, 83, 84, 85, 86, 88, 89, 91, 92, 93, 94, 95, 96, 98, 99, 100, 200, 300, 400, 500, 600, 800, 900

Offset: 1

Marc Groz, May 13 2024

There are 107 terms, considering all terms up to 10^66 using English names of large numbers and various conventional extensions thereof (see Wikipedia link), since quadrillion, quintillion, etc. each have three or more syllables themselves. Terms like "one googol" (or possibly "a googol"), "two googol," ..., "twelve googol" are unconventional, hence disallowed. - Michael S. Branicky, May 28 2024

			a(2) = 17 is the second number whose name in American English has exactly three syllables: "seventeen".

Michael S. Branicky, Table of n, a(n) for n = 1..107
Wikipedia, Names of Large Numbers

Cf. A075774, A180961.

# uses function in A075774
print([k for k in range(501) if A075774(k) == 3]) # Michael S. Branicky, May 27 2024

A075774(a(n)) = 3. - Michael S. Branicky, May 27 2024

A164043 Numbers divisible by the number of syllables in their (American) English name.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 14, 16, 18, 20, 21, 24, 30, 33, 36, 39, 40, 42, 45, 48, 50, 51, 54, 60, 63, 66, 69, 72, 76, 80, 81, 84, 90, 93, 96, 99, 104, 108, 112, 115, 120, 126, 130, 132, 138, 140, 144, 147, 150, 156, 160, 162, 168, 175, 180, 186, 190, 192, 198

Offset: 1

Jonathan Vos Post, Aug 08 2009

The name has no extra "and" syllables, as in 104 being in this sequence because "one hundred four" has 4 syllables (which divides 104) rather than "one hundred and four" which has 5 syllables.

			a(15) = 21 because "twenty-one" has 3 syllables, and 3*7 = 21.

Index to OEIS: sequences related to English words for n

Cf. A075774, A045736, A002810 (British variant), A163648.

# uses function in A075774
def ok(n): return n and n%A075774(n) == 0
print([k for k in range(200) if ok(k)]) # Michael S. Branicky, May 27 2024

{k such that A075774(k)|k}.

84 inserted and more terms from Michael S. Branicky, May 27 2024

A231072 Number of words in English spelling of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2

Offset: 0

M. F. Hasler, Nov 03 2013

From a(101) on it must be made precise that this sequence uses the American style ("one hundred one"), as in A052360, and not the British style ("one hundred and one"). The choice of long or short scale does not make a difference since, e.g., the word "milliard" in long scale use would simply be replaced by "billion" in short scale. However, the use of "thousand [million]" instead, would lead to different results for numbers such that floor(n/10^6) mod 10^3 is zero. - M. F. Hasler, Nov 03 2013

			From "zero" to "twenty", the numbers are written in one word, so a(0..20)=1. "Twenty-one" is the first term to require 2 words, so a(21)=2.

Index to OEIS: sequences related to English words for n

Cf. A001167, A075774, A052360.

a(n)=sum(k=7,#n=Vecsmall(English(n)),n[k-3]<65)+1 \\ See A052360 for English(). Only characters 4,...,length-4 need to be checked for space/hyphen since there is no word with less than 3 letters.

A249030 The difference between the number of letters and the number of syllables in n in English. (Omit "and" in both.)

Original entry on oeis.org

2, 2, 2, 4, 3, 3, 2, 3, 4, 3, 2, 3, 5, 6, 6, 5, 5, 6, 6, 6, 4, 6, 6, 8, 7, 7, 6, 7, 8, 7, 4, 6, 6, 8, 7, 7, 6, 7, 8, 7, 3, 5, 5, 7, 6, 6, 5, 6, 7, 6, 3, 5, 5, 7, 6, 6, 5, 6, 7, 6, 3, 5, 5, 7, 6, 6, 5, 6, 7, 6, 4, 6, 6, 8, 7, 7, 6, 7, 8, 7

Offset: 0

Chris Smith, Oct 27 2014

Take the number of letters in the spelling of a number and subtract the number of syllables in the sounding of that number. For example, zero has four letters and two syllables generating 4-2=2 for the first term. As such it is linked to sequences A005589 and A075774.

Cf. A005589, A075774.

a(n) = A005589(n) - A075774(n).

Corrected a(11) and extended to a(79) by Chris Smith, Mar 16 2015

cp's OEIS Frontend

A002810 Smallest number containing n syllables in UK English.

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A089746 Period 12: repeat (4, 4, 1, 2, 1, 1, 2, 2, 3, 3, 3, 3). (Number of syllables in English name of the months.)

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A163648 Primes p with a prime number of syllables in their name in American English.

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A045736 Smallest positive integer requiring n syllables to pronounce in American English.

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A180961 Numbers such that the American English name of the number has four syllables.

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A230956 Semiprimes k with a semiprime number of syllables in their name in American English.

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A372807 Numbers whose American English name has exactly three syllables.

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