login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note that a(n) <= 4 by Lagrange's four-square 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)