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Number of letters in the Hindi word for the number n.
0

%I #26 May 29 2019 12:55:32

%S 4,2,2,3,3,4,2,3,3,2,2,5,4,4,4,5,4,4,5,5,3,5,4,4,5,5,5,6,6,5,3,5,5,6,

%T 6,6,5,6,5,7,5,7,6,8,8,8,7,8,7,5,4,6,4,6,4,4,4,6,6,4,3,4,4,5,5,5,6,4,

%U 4,6,4,6,5,6,6,6,6,6,6,5,4,6,5,6,6,5,6

%N Number of letters in the Hindi word for the number n.

%C From _Sangeet Paul_, May 29 2019: (Start)

%C What constitutes a distinct letter is determined by the following rules: all words are in Modern Standard Hindi written in the Devanagari script; a vowel, a vowel diacritic, a consonant, a consonant diacritic, or a nasal diacritic is one letter; a conjunct consonant is as many letters as the consonants conjuncted; a nuqta or a halant is not a letter; and a space between two words is not a letter.

%C Hindi has a unique word for every number from 0 to 99, and a unique place-value word for 100 and every power of 10 of the form 10^(2k+1) where k is a positive integer. Therefore:

%C a(n) = a(n mod 100) + (d(100) + a(floor(n/100) mod 10))*[floor(n/100) mod 10 > 0] + Sum_{k=1..oo} (d(10^(2k+1)) + a(floor(n/(10^(2k+1))) mod 100))*[floor(n/(10^(2k+1))) mod 100 > 0] where [] is the Iverson bracket and d() is the number of letters in a place-value word.

%C d(100) = 2, d(10^3) = 4, d(10^5) = 3, d(10^7) = 4, d(10^9) = 3, d(10^11) = 3, d(10^13) = 3, d(10^15) = 3, d(10^17) = 3.

%C In another popular convention: a vowel, or a consonant is one letter; a consonant diacritic is half a letter; a conjunct consonant is half a letter plus half as many letters as the consonants conjuncted; and a vowel diacritic, a nasal diacritic, a nuqta, a halant, or a space is not a letter. These rules change the sequence to: 2.5, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 3.5, 3, 3, 3, 3, 3, 3.5, 4, 3.5, 2, ...

%C (End)

%H Author?, <a href="http://www.hindidevanagari.com/numbers_saNkhyaaENn.html">Hindi Numbers</a>

%H Critical Languages Center, Univ. Alabama, <a href="http://bama.ua.edu/~clc/hindi/numbers_hindi.html">Numbers in Hindi</a>

%H WikiBooks, <a href="http://en.wikibooks.org/wiki/Hindi:Numbers">Hindi Numbers</a>

%H <a href="/index/Lc#letters">Index entries for sequences related to number of letters in n</a>

%H <a href="/index/Na">Index entries for sequences related to names of numbers</a>

%Y Cf. A005589.

%K nonn,word

%O 0,1

%A _Vinay Vaishampayan_, Jun 19 2008, Jun 20 2008

%E Links added by _N. J. A. Sloane_, Jun 20 2008

%E Offset 0 from _Sangeet Paul_, May 27 2019

%E a(21)-a(86) from _Sangeet Paul_, May 29 2019