A045736 -id:A045736 - 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

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

cp's OEIS Frontend

A002810 Smallest number containing n syllables in UK English.

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