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A188112 Integers of the form x^2+xy+2y^2,with x and y nonnegative, with repetitions. 1

%I #20 Nov 21 2013 12:50:08

%S 0,1,2,4,4,8,8,9,11,14,16,16,18,22,22,23,25,28,32,32,32,36,36,37,43,

%T 44,44,46,49,50,53,56,56,58,58,64,64,64,71,72,72,74,74,77,79,81,86,88,

%U 88,88,92,92,98,99,100,100,106,106,107,109,112,112,116,116,121,126,127

%N Integers of the form x^2+xy+2y^2,with x and y nonnegative, with repetitions.

%C Primes appear only once.

%H Vincenzo Librandi, <a href="/A188112/b188112.txt">Table of n, a(n) for n = 1..1000</a>

%e {n,x,y}: {0,0,0},...,{4,1,1},{4,2,0},{8,0,2},{8,2,1},...,{11,1,2},{14,3,1}.

%t f[upto_]:=Module[{max=Floor[Sqrt[upto]],s}, s=Sort[First[#]^2+ Times@@#+2Last[#]^2&/@Tuples[Range[0,max],{2}]]; Select[s, #<=upto&]]; f[150] (* _Harvey P. Dale_, Mar 28 2011 *)

%Y Cf. A106856, primes of the form x^2+xy+2y^2, with x and y nonnegative.

%K nonn,easy

%O 1,3

%A _Zak Seidov_, Mar 21 2011

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)