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A002810 Smallest number containing n syllables in UK English.

%I A002810 M4341 N1818 #68 Feb 16 2025 08:32:26
%S A002810 1,7,11,27,77,107,111,127,177,777,1127,1177,1777,7777,11777,27777,
%T A002810 77777,107777,111777,127777,177777,777777,1127777,1177777,1777777,
%U A002810 7777777,11777777,27777777,77777777,107777777,111777777,127777777,177777777,777777777
%N A002810 Smallest number containing n syllables in UK English.
%C A002810 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
%C A002810 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
%C A002810 From _Bernard Schott_, Feb 18 2019: (Start)
%C A002810 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.
%C A002810 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)
%D A002810 Rodolfo Kurchan, Mesmerizing Math Puzzles, by Sterling Publications, 2000, p. 18.
%D A002810 R. C. Penner, Discrete Mathematics, Proofs Techniques and Mathematical Structures, World Scientific, 1999, Reprinted 2001, p. 97.
%D A002810 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002810 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002810 David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Revised edition, 1997, p. 171.
%H A002810 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BerryParadox.html">Berry Paradox</a>
%H A002810 Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_one">one hundred one</a> (US)
%H A002810 Wiktionary, <a href="https://en.wiktionary.org/wiki/one_hundred_and_one">one hundred and one</a> (UK)
%H A002810 Robert G. Wilson v, <a href="/A000027/a000027.txt">English names for the numbers from 0 to 11159 without spaces or hyphens</a>.
%H A002810 <a href="/index/El#English">Index to OEIS: sequences related to English words for n</a>
%F A002810 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
%e A002810 "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.
%o A002810 (PARI) 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
%Y A002810 Cf. A045736.
%K A002810 word,nonn
%O A002810 1,2
%A A002810 _N. J. A. Sloane_
%E A002810 Edited and extended by _M. F. Hasler_, Nov 03 2013