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%I M0959 #45 Oct 24 2023 23:15:50
%S 1,2,4,5,7,8,10,13,15,16,20,23,25,28,31,32,37,39,40,47,52,55,58,60,63,
%T 64,71,79,80,85,87,92,95,100,103,111,112,119,124,127,128,130,135,143,
%U 148,151,156,159,160,167,175,183,188,191,199,207,208,215,220,223,231
%N Positive numbers that are not the sum of three nonzero squares.
%C Not of the form x^2 + y^2 + z^2 with x, y, z >= 1.
%C Complement of A000408, but skipping the zero. - _R. J. Mathar_, Nov 23 2006
%C A025427(a(n)) = 0. - _Reinhard Zumkeller_, Feb 26 2015
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Ray Chandler, <a href="/A004214/b004214.txt">Table of n, a(n) for n = 1..10000</a>
%H David S. Bettes, <a href="/A004214/a004214.pdf">Letter to N. J. A. Sloane, Nov 05 1976</a>.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e The smallest numbers that are the sums of 3 nonzero squares are 3=1+1+1, 6=1+1+4, 9=1+4+4, etc.
%p gf := sum(sum(sum(q^(x^2+y^2+z^2), x=1..25), y=1..25), z=1..25): s := series(gf, q, 500): for n from 1 to 500 do if coeff(s, q, n)=0 then printf(`%d,`,n) fi:od:
%t f[n_] := Flatten[Position[Take[Rest[CoefficientList[Sum[x^(i^2), {i, n}]^3, x]], n^2], 0]];f[16] (* _Ray Chandler_, Dec 06 2006 *)
%o (PARI) isA000408(n)={ local(a,b) ; a=1; while(a^2+1<n, b=1 ; while(b<=a && a^2+b^2<n, if(issquare(n-a^2-b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0) ; }
%o isA004214(n)={ return(! isA000408(n)) ; }
%o n=1 ; for(an=1,20000, if(isA004214(an), print(n," ",an); n++)) \\ _R. J. Mathar_, Nov 23 2006
%o (Haskell)
%o a004214 n = a004214_list !! (n-1)
%o a004214_list = filter ((== 0) . a025427) [1..]
%o -- _Reinhard Zumkeller_, Feb 26 2015
%Y Cf. A000408, A025427.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, Apr 20 2001
%E Name clarified by _Wolfdieter Lang_, Apr 04 2013
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