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%I #19 Aug 01 2018 06:25:54
%S 4,8,9,12,13,16,17,18,20,21,22,24,25,26,27,28,29,30,31,32,33,34,35,36,
%T 37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,
%U 60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82
%N Numbers which can be written as sum of squares>1.
%C A078134(a(n))>0.
%C Numbers which can be written as a sum of squares of primes. - _Hieronymus Fischer_, Nov 11 2007
%C Equivalently, numbers which can be written as a sum of squares of 2 and 3. Proof for numbers m>=24: if m=4*(k+6), k>=0, then m=(k+6)*2^2; if m=4*(k+6)+1 than m=(k+4)*2^2+3^2; if m=4*(k+6)+2 then m=(k+2)*2^2+2*3^2; if m=4*(k+6)+3 then m=k*2^2+3*3^2. Clearly, the numbers a(n)<24 can also be written as sums of squares of 2 and 3. Explicit representation as a sum of squares of 2 and 3 for numbers m>23: m=c*2^2+d*3^2, where c:=((floor(m/4) - 2*(m mod 4))>=0 and d:=m mod 4. - _Hieronymus Fischer_, Nov 11 2007
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SquareNumber.html">Square Number</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n)=n + 12 for n >= 12. - _Hieronymus Fischer_, Nov 11 2007
%t Join[{4, 8, 9, 12, 13, 16, 17, 18, 20, 21, 22}, Range[24, 82]] (* _Jean-François Alcover_, Aug 01 2018 *)
%o (PARI) a(n)=if(n>11,n+12,[4,8,9,12,13,16,17,18,20,21,22][n]) \\ _Charles R Greathouse IV_, Aug 21 2011
%Y Complement of A078135.
%Y Cf. A000290, A078136, A078131, A001597, A025475, A078134, A078135, A078139, A090677, A134600, A134605, A134608, A134612, A134616, A134618, A134620.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, Nov 19 2002
%E Edited by _N. J. A. Sloane_, Oct 17 2009 at the suggestion of R. J. Mathar.
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