

A088910


Conjectured minimal required number k of terms in a representation n=sum_(i=1..k)e_i*(p_i)^2 by distinct primes p_i, where e_i is 1 or 1.


3



4, 3, 4, 4, 1, 2, 5, 5, 4, 1, 4, 4, 3, 2, 4, 3, 2, 5, 5, 4, 3, 2, 4, 3, 2, 1, 4, 4, 3, 2, 3, 5, 4, 3, 2, 4, 3, 4, 3, 3, 2, 5, 5, 4, 3, 2, 4, 3, 2, 1, 4, 4, 3, 2, 3, 5, 4, 3, 2, 4, 5, 4, 3, 3, 4, 3, 5, 4, 3, 4, 3, 3, 2, 3, 2, 4, 3, 4, 3, 4, 4, 3, 4, 3, 5, 4, 4, 3, 4, 5, 5, 4, 3, 4, 4, 3, 2, 3, 4, 4, 3, 4, 5, 5, 4
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OFFSET

0,1


COMMENTS

It is conjectured that all sequence terms are <=5. The terms with a(n)=5 were provided by W. Edwin Clark.


REFERENCES

Robert E. Dressler, Louis Pigno, Robert Young, Sums of squares of primes. Nordisk Mat. Tidskr. 24 (1976), no. 1, 3940.


LINKS

Table of n, a(n) for n=0..104.
Hugo Pfoertner, Conjectured minimal representations of n by squaresof distinct primes (Table for n<=400).


EXAMPLE

The following are representation with the minimal number of terms:
a(0)=4: 0=7^211^217^2+19^2, a(1)=3: 1=7^2+11^213^2, a(4)=1: 4=2^2,
a(5)=2: 5=3^22^2, a(6)=5: 6=(2^2)+3^2+7^2+11^213^2.


CROSSREFS

Cf. A088934 maximum required prime in representation, A048261, A088908, A088909.
Sequence in context: A241928 A111048 A016700 * A010308 A200625 A156743
Adjacent sequences: A088907 A088908 A088909 * A088911 A088912 A088913


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Oct 24 2003


STATUS

approved



