A100559 Smallest prime equal to the sum of n distinct squares.

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

Links

Table of n, a(n) for n=2..42.

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

Adjacent sequences: A100556 A100557 A100558 * A100560 A100561 A100562

Keyword

nonn,easy

Author

Giovanni Teofilatto, Jan 02 2005

Extensions

More terms from T. D. Noe, Jan 04 2005

Status

approved