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%I #18 Mar 18 2021 08:22:59
%S 0,0,0,0,2,0,2,4,1,4,0,3,8,2,7,0,6,11,4,10,2,8,0,6,14,3,12,0,9,18,6,
%T 15,2,12,23,8,20,4,16,0,12,24,7,20,2,15,30,10,25,4,20,35,14,30,8,24,1,
%U 18,36,11,30,4,23,42,16,35,8,28,0,20,42,12,34,3
%N a(n) = x(n) mod floor(sqrt(x(n))), where x(n) = floor((n^2)/2).
%H Simon Strandgaard, <a href="/A338227/a338227.jpg">Plot of 10000 terms with primes highlighted</a>
%F a(n) = A007590(n) mod A000196(A007590(n)).
%F a(n) = A007590(n) mod A049472(n). - _Kevin Ryde_, Jan 30 2021
%e x( 7) = floor(( 7^2)/2) = 24, a( 7) = 24 mod floor(sqrt(24)) = 24 mod 4 = 0,
%e x( 8) = floor(( 8^2)/2) = 32, a( 8) = 32 mod floor(sqrt(32)) = 32 mod 5 = 2,
%e x( 9) = floor(( 9^2)/2) = 40, a( 9) = 40 mod floor(sqrt(40)) = 40 mod 6 = 4,
%e x(10) = floor((10^2)/2) = 50, a(10) = 50 mod floor(sqrt(50)) = 50 mod 7 = 1.
%t x[n_] := Floor[(n^2)/2]; A338227[n_] := Mod[x[n], Floor[Sqrt[x[n]]]]; Table[A338227[n], {n, 2, 75}] (* _Robert P. P. McKone_, Jan 31 2021 *)
%o (Ruby) values = Array.new(50) do |i|
%o x = ((i + 2) ** 2) / 2
%o x % Integer.sqrt(x)
%o end
%o p values
%o (PARI) a(n) = my(x=n^2\2); x % sqrtint(x); \\ _Michel Marcus_, Jan 31 2021
%Y Cf. A000196, A007590, A049472.
%K nonn
%O 2,5
%A _Simon Strandgaard_, Jan 30 2021
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