

A100876


Least number of squares that sum to prime(n).


0



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
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OFFSET

1,1


COMMENTS

Note that a(n) <= 4 by Lagrange's foursquare theorem.  T. D. Noe, Jan 10 2005
Primes 2 and 4k+1 (A002313) require only 2 positive squares; primes 8k+3 (A007520) require 3 positive squares; primes 8k+7 (A007522) require 4 positive squares.


LINKS

Table of n, a(n) for n=1..105.


FORMULA

a(n) = A002828(prime(n))  T. D. Noe, Jan 10 2005


EXAMPLE

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.


MATHEMATICA

SquareCnt[n_] := If[SquaresR[1, n] > 0, 1, If[SquaresR[2, n] > 0, 2, If[SquaresR[3, n] > 0, 3, 4]]]; Table[p = Prime[n]; SquareCnt[p], {n, 150}] (* T. D. Noe, Jan 10 2005, revised Sep 27 2011 *)


CROSSREFS

Cf. A002828 (least number of squares needed to represent n).
Sequence in context: A308566 A288535 A105117 * A089215 A238766 A325239
Adjacent sequences: A100873 A100874 A100875 * A100877 A100878 A100879


KEYWORD

nonn


AUTHOR

Giovanni Teofilatto, Jan 09 2005


EXTENSIONS

More terms from T. D. Noe, Jan 10 2005


STATUS

approved



