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A048761
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Smallest square greater than or equal to n.
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19
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0, 1, 4, 4, 4, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 25, 25, 25, 25, 25, 25, 25, 25, 25, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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For each k > 0, the term k^2 is listed 2k - 1 times.
a(n+1) is the least square greater than n. (End)
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REFERENCES
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Krassimir Atanassov, On the 40th and 41st Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 4, No. 3 (1998), 101-104.
J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, 202-204.
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n)^2 = 2*zeta(3) - Pi^4/90. - Amiram Eldar, Aug 15 2022
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MAPLE
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ceil(sqrt(n)) ;
%^2 ;
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MATHEMATICA
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PROG
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(Haskell)
a048761 n = (a000196 n + 1 - a010052 n) ^ 2
a048761_list = 0 : concat (f 1 1) where
f u v = (take v $ repeat u) : f (u + v + 2) (v + 2)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Charles T. Le (charlestle(AT)yahoo.com)
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EXTENSIONS
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STATUS
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approved
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