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A022846
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Nearest integer to n*sqrt(2).
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12
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0, 1, 3, 4, 6, 7, 8, 10, 11, 13, 14, 16, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 33, 34, 35, 37, 38, 40, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 68, 69, 71, 72, 74, 75, 76, 78, 79, 81, 82, 83, 85, 86, 88, 89, 91, 92, 93, 95, 96
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Let R(i,j) be the rectangle with antidiagonals 1; 2,3; 4,5,6; ...; n^2 is in antidiagonal number a(n). Proof: n^2 is in antidiagonal m iff A000217(m-1)< n^2 <=A000217(m), where A000217(m)=m*(m+1)/2. So m = A002024(n^2) = round(n*sqrt(2)) = a(n). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Mar 07 2003
In the rectangle R(i,j), n^2 is the number in row i=A057049(n) and column j=A057050(n), so that for n>=1, a(n) = -1+A057049(n)+A057050(n). [From Clark Kimberling, Jan 31 2011]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| a(n)=A002024(n^2).
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PROG
| (PARI) a(n)=floor(1/2+n*sqrt(2))
(MAGMA) [Round(n*Sqrt(2)): n in [0..60]]; // Vincenzo Librandi, Oct 22 2011
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CROSSREFS
| A063957 (complement of this set).
Sequence in context: A047299 A186159 A184578 * A083922 A039042 A007378
Adjacent sequences: A022843 A022844 A022845 * A022847 A022848 A022849
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KEYWORD
| nonn,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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