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Search: id:A100559
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| A100559 |
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Smallest prime equal to the sum of n distinct squares. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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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 (noe(AT)sspectra.com), Jan 04 2005
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EXAMPLE
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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.
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MATHEMATICA
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$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)
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CROSSREFS
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Adjacent sequences: A100556 A100557 A100558 this_sequence A100560 A100561 A100562
Sequence in context: A103094 A108928 A097812 this_sequence A087348 A050409 A111937
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KEYWORD
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nonn,easy
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Jan 02 2005
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 04 2005
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