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A100559
Smallest prime equal to the sum of n distinct squares.
1
5, 29, 71, 79, 131, 179, 269, 349, 457, 569, 719, 971, 1171, 1327, 1601, 1913, 2269, 2593, 2999, 3539, 4099, 4549, 5231, 5717, 6529, 7297, 7879, 8779, 9791, 10711, 11867, 12809, 14081, 15269, 16561, 17863, 19463, 20771, 22541, 24329, 25913
OFFSET
2,1
COMMENTS
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
EXAMPLE
a(3)=29 because 29=2^2+3^2+4^2;
a(4) = 71 = 1^2+3^2+5^2+6^2
a(5)=79 because 79=1^2+2^2+3^2+4^2+7^2.
MATHEMATICA
$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)
CROSSREFS
Sequence in context: A108928 A097812 A176333 * A224498 A087348 A154412
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Jan 02 2005
EXTENSIONS
More terms from T. D. Noe, Jan 04 2005
STATUS
approved