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%I #4 Mar 30 2012 18:39:59
%S 5,29,71,79,131,179,269,349,457,569,719,971,1171,1327,1601,1913,2269,
%T 2593,2999,3539,4099,4549,5231,5717,6529,7297,7879,8779,9791,10711,
%U 11867,12809,14081,15269,16561,17863,19463,20771,22541,24329,25913
%N Smallest prime equal to the sum of n distinct squares.
%C The Mathematica code uses backtracking to find the least prime for each n. The Print command may be uncommented to show the sum that produces the prime. - _T. D. Noe_, Jan 04 2005
%e a(3)=29 because 29=2^2+3^2+4^2;
%e a(4) = 71 = 1^2+3^2+5^2+6^2
%e a(5)=79 because 79=1^2+2^2+3^2+4^2+7^2.
%t $RecursionLimit=1000; try2[lev_] := Module[{t, j, ss}, ss=Plus@@(Take[soln, lev-1]^2); If[lev>n, If[ss<=minPrime&&PrimeQ[ss], minPrime=ss; bestSoln={ss, soln}], If[lev==1, t=1, t=soln[[lev-1]]+1]; j=t; While[ss+Sum[(j+i)^2, {i, 0, n-lev}] <= minPrime, soln[[lev]]=j; try2[lev+1]; soln[[lev]]=t; j++ ]]]; Table[minPrime=Infinity; bestSoln={}; soln=Table[1, {n}]; try2[1]; (*Print[bestSoln];*) bestSoln[[1]], {n, 2, 50}] (T. D. Noe)
%K nonn,easy
%O 2,1
%A _Giovanni Teofilatto_, Jan 02 2005
%E More terms from _T. D. Noe_, Jan 04 2005
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