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Search: id:A140716
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| A140716 |
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Blocky integers, i.e. integers n>1 such that there is a run of n consecutive integer squares the average of which is a square. |
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+0
1
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| 7, 25, 31, 49, 55, 73, 79, 97, 103, 121, 127, 145, 151, 169, 175, 193, 199, 217, 223, 241, 247, 265, 271, 289, 295, 313, 319, 337, 343, 361, 367, 385, 391, 409, 415, 433, 439, 457, 463, 481, 487, 505, 511, 529, 535, 553, 559, 577, 583
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For a blocky n, a starting k^2 in the required run of squares is obtained by taking k = a - b - (n-1)/2, where ab=(n^2 - 1)/48.
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REFERENCES
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S. Marivani and others, Problem 11227, Amer. Math. Monthly, 115, No. 6, 2008, 568-569.
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FORMULA
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n is blocky if and only if n>1 and n (mod 24) = 1 or -1 or 7 or -7.
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EXAMPLE
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7 is blocky because [(-3)^2 + (-2)^2 + (-1)^2 + 0^2 + 1^2 + 2^2 + 3^2]/7=28/7=4=2^2.
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MAPLE
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a:=proc(n) if `mod`(n, 24)=1 or `mod`(n, 24)=-1 or `mod`(n, 24)=7 or `mod`(n, 24) =-7 then n else end if end proc: seq(a(n), n=2..600);
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CROSSREFS
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Sequence in context: A065660 A100496 A110081 this_sequence A141393 A075927 A119617
Adjacent sequences: A140713 A140714 A140715 this_sequence A140717 A140718 A140719
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 04 2008
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