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


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

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

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

%C 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.

%C There are no more terms < 10^7. - _Donovan Johnson_, Jun 27 2012

%C There are no more terms < 4*10^9. - _Jud McCranie_, Jun 09 2013

%C There are no more terms < 10^11. - _Giovanni Resta_, Jun 09 2013

%D 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.

%o (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)

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

%K nonn,hard,more

%O 1,2

%A _Charles R Greathouse IV_, Jun 21 2012

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Last modified October 14 14:26 EDT 2019. Contains 328018 sequences. (Running on oeis4.)