A212292 Odd numbers not of the form p^2 + q^2 + r with p, q, and r prime.

1, 3, 5, 7, 9, 17, 33, 43, 83, 179, 623, 713, 1019

Offset: 1

Author

Charles R Greathouse IV, Jun 21 2012

Keywords

• nonn
• hard
• more

Comments

The corresponding sequence with the restriction to primes removed is empty.

Wang shows that all but x^{9/20+e} members of this sequence up to x are congruent to 2 mod 3, for any e > 0.

There are no more terms < 10^7. - Donovan Johnson, Jun 27 2012

There are no more terms < 4*10^9. - Jud McCranie, Jun 09 2013

There are no more terms < 10^11. - Giovanni Resta, Jun 09 2013

References

• Wang Mingqiang, On sums of a prime, and a square of prime, and a k-power of prime, Northeastern Mathematical Journal 18:4 (2002), pp. 283-286.

Crossrefs

Cf. A045636, A006285, A118955, A156695, A226484.

Programs

PARI

list(lim)=my(p1=vector(primepi(sqrt(lim-5.5)),i,prime(i)^2), p2=List(), v=List(), u=List([1,3,5,7,9]), t); for(i=1,#p1, for(j=i,#p1,t=p1[i]+p1[j]; if(t>lim, break, listput(p2,t)))); p2=vecsort(Vec(p2),,8); for(i=1,#p2,forprime(p=2,lim-p2[i],listput(v,p2[i]+p))); v=select(n->n%2, vecsort(Vec(v),,8)); for(i=2,#v,forstep(j=v[i-1]+2,v[i]-2,2,listput(u,j))); Vec(u)