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A256944
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Squares which are not the sums of two consecutive nonsquares.
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4
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0, 1, 4, 9, 16, 36, 49, 64, 100, 144, 196, 256, 289, 324, 400, 484, 576, 676, 784, 900, 1024, 1156, 1296, 1444, 1600, 1681, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056, 7396, 7744, 8100, 8464
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OFFSET
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1,3
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COMMENTS
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The union of A008843, A055792, and A016742. [Corrected by Charles R Greathouse IV, May 07 2015]
Consists of the squares of all even numbers and odd numbers in A078057 = (1, 3, 7, 17, 41, 99, ...), see also A001333 = abs(A123335). See A257282 for the square roots and A257292 for their complement in the nonnegative integers A001477. - M. F. Hasler, May 08 2015
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) ~ 4n^2. - Charles R Greathouse IV, May 07 2015
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EXAMPLE
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0, 1, 4, 9, 16, 36, are in this sequence because first 14 sums of two consecutive nonsquares are 5, 8, 11, 13, 15, 18, 21, 23, 25, 27, 29, 32, 35, 37.
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MATHEMATICA
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lim = 15000; s = Plus @@@ (Partition[#, 2, 1] & @ Complement[Range@ lim, Range[Floor@ Sqrt[lim]]^2]); Select[Range@ Floor[Sqrt[lim]]^2, !MemberQ[s, #] &] (* Michael De Vlieger, Apr 29 2015 *)
lst=Partition[Select[Range[0, 10^6], !IntegerQ[Sqrt[#]]&], 2, 1]/.{a_, b_}-> a+b; a256944=Complement[Table[n^2, {n, 0, Sqrt[Last[lst]]}], lst] (* timing improved by Ivan N. Ianakiev, Apr 30 2015 *)
Union[#, Range[0, Max@ #, 2]] &@ Numerator[Convergents[Sqrt@ 2, 6]]^2 (* Michael De Vlieger, Aug 06 2016, after Harvey P. Dale at A001333 *)
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PROG
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(PARI) is(n)=issquare(n) && (n%2==0 || issquare(n\2) || issquare(n\2+1)) \\ Charles R Greathouse IV, May 07 2015
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CROSSREFS
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Cf. A000037, A000290, A008843, A016742, A056792, A257282.
Sequence in context: A100498 A068952 A000548 * A349062 A106575 A025620
Adjacent sequences: A256941 A256942 A256943 * A256945 A256946 A256947
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KEYWORD
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nonn,easy
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AUTHOR
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Juri-Stepan Gerasimov, Apr 25 2015
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STATUS
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approved
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