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Search: id:A100876
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| A100876 |
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Least number of squares that sum to prime(n). |
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+0
1
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| 2, 3, 2, 4, 3, 2, 2, 3, 4, 2, 4, 2, 2, 3, 4, 2, 3, 2, 3, 4, 2, 4, 3, 2, 2, 2, 4, 3, 2, 2, 4, 3, 2, 3, 2, 4, 2, 3, 4, 2, 3, 2, 4, 2, 2, 4, 3, 4, 3, 2, 2, 4, 2, 3, 2, 4, 2, 4, 2, 2, 3, 2, 3, 4, 2, 2, 3, 2, 3, 2, 2, 4, 4, 2, 3, 4, 2, 2, 2, 2, 3, 2, 4, 2, 4, 3, 2, 2, 2, 4, 3, 4, 4, 3, 3, 4, 2, 2, 3, 2, 3, 2, 3, 2, 3
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Note that a(n) <= 4 by Lagrange's four-square theorem. - T. D. Noe (noe(AT)sspectra.com), Jan 10 2005
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FORMULA
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a(n) = A002828(prime(n)) - T. D. Noe (noe(AT)sspectra.com), Jan 10 2005
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EXAMPLE
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a(2)=3 because 3=1^2+1^2+1^2;
a(3)=2 because 5=1^2+2^2;
a(4)=4 because 7=2^2+1^2+1^2+1^2.
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MATHEMATICA
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Needs["NumberTheory`NumberTheoryFunctions`"]; SquareCnt[n_] := If[SumOfSquaresR[1, n]>0, 1, If[SumOfSquaresR[2, n]>0, 2, If[SumOfSquaresR[3, n]>0, 3, 4]]]; Table[p=Prime[n]; SquareCnt[p], {n, 150}] (T. D. Noe)
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CROSSREFS
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Cf. A002828 (least number of squares needed to represent n).
Sequence in context: A058973 A155520 A105117 this_sequence A089215 A070296 A072645
Adjacent sequences: A100873 A100874 A100875 this_sequence A100877 A100878 A100879
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KEYWORD
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nonn
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AUTHOR
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Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), Jan 09 2005
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EXTENSIONS
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More terms from T. D. Noe (noe(AT)sspectra.com), Jan 10 2005
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