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A140395
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Number of letters in the Hindi word for the number n.
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0
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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, 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, 4, 6, 4, 6, 5, 6, 6, 6, 6, 6, 6, 5, 4, 6, 5, 6, 6, 5, 6
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OFFSET
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0,1
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COMMENTS
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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.
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:
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.
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.
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, ...
(End)
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LINKS
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CROSSREFS
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KEYWORD
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nonn,word
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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