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%I #14 Aug 11 2016 05:49:45
%S 0,1,2,3,4,6,7,8,10,12,14,16,17,18,20,22,24,26,28,30,32,34,36,38,40,
%T 41,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,
%U 86,88,90,92,94,96,98,99,100,102,104,106,108,110,112,114,116
%N Numbers whose square is not the sum of two consecutive nonsquares.
%C See A256944 for further information.
%C Union of even integers and A001333. - _Ivan Neretin_, Aug 04 2016
%H Ivan Neretin, <a href="/A257282/b257282.txt">Table of n, a(n) for n = 1..10001</a>
%F a(n) = sqrt(A256944).
%F a(n) ~ 2n. [Following _Charles R Greathouse IV_'s formula for A256944.]
%e 5 is not in the sequence because 5^2 = 25 = 12 + 13 is the sum of two consecutive numbers both of which are not squares.
%e All even numbers are in the sequence because (2k)^2 = 4k^2 cannot be written as sum of two consecutive numbers and 2k^2 is not a square.
%e An odd number n is in the sequence if one of the two numbers next to n^2/2 is a square.
%t Union[#, Range[0, Max@ #, 2]] &@ Numerator[Convergents[Sqrt@ 2, 7]] (* _Michael De Vlieger_, Aug 06 2016, after _Harvey P. Dale_ at A001333 *)
%o (PARI) is(n)={n%2==0 || issquare(n^2\2) || issquare(n^2\2+1)}
%Y Cf. A256944.
%K nonn,easy
%O 1,3
%A _M. F. Hasler_, May 08 2015
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