A183214 Least number of squared primes that add up to n; -1 if impossible.

0, -1, -1, -1, 1, -1, -1, -1, 2, 1, -1, -1, 3, 2, -1, -1, 4, 3, 2, -1, 5, 4, 3, -1, 6, 1, 4, 3, 7, 2, 5, 4, 8, 3, 2, 5, 4, 4, 3, 6, 5, 5, 4, 3, 6, 5, 5, 4, 7, 1, 2, 5, 4, 2, 3, 6, 5, 3, 2, 3, 6, 4, 3, 4, 7, 5, 4, 3, 4, 6, 5, 4, 5, 7, 2, 3, 4, 5, 3, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 4, 5, 6, 6, 5, 6, 2, 3, 4, 5, 3, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 4, 5, 6, 6, 5, 1, 7, 3, 4, 2, 6, 4, 5, 3, 2, 5, 4, 4, 3, 6, 5, 5, 4, 3, 6, 5, 5, 4, 7, 6, 2, 3, 4, 5, 3, 4, 5, 6, 4, 3, 4, 5, 5, 4, 5, 6, 6, 5, 4, 5, 6, 6, 5, 1, 2, 3, 4, 2, 3, 4, 5, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4, 3, 4, 5, 5, 4, 5, 6

Offset

0,9

Comments

a(n)<=8 for n<10^9, with a(n)=8 for 3703393 values <=10^9.

Conjecturally, a(n)<=8 with a(n)=8 infinitely often.

a(n)>0 for n>23. This follows from n=4j+9k for j,k>=0.

If a(n)!=-1 then a(n)>=A002828(n). - David W. Wilson, Sep 07 2016

Links

David W. Wilson, Table of n, a(n) for n = 0..10000

Example

a(17)=3 since 17=2^2+2^2+3^2. a(29)=2 since 29=2^2+5^2.

Mathematica

Table[Min[Length /@ Select[Map[DeleteCases[#, k_ /; ! PrimeQ@ Sqrt@ k] &, IntegerPartitions@ n], Total@ # == n &] /. {} -> {-1}], {n, 0, 50}] (* Michael De Vlieger, Sep 08 2016 *)

Crossrefs

Cf. A002828, A183215, A183216.

Sequence in context: A284345 A347463 A337619 * A346009 A344756 A101221

Adjacent sequences: A183211 A183212 A183213 * A183215 A183216 A183217

Keyword

sign

Author

Dmitry Kamenetsky, Jan 01 2011

Extensions

a(0) added by David W. Wilson, Sep 07 2016

Status

approved