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A212292 Odd numbers not of the form p^2 + q^2 + r with p, q, and r prime. 2
1, 3, 5, 7, 9, 17, 33, 43, 83, 179, 623, 713, 1019 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..13.

PROG

(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)

CROSSREFS

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

Sequence in context: A191356 A144753 A220221 * A270837 A057482 A114136

Adjacent sequences:  A212289 A212290 A212291 * A212293 A212294 A212295

KEYWORD

nonn,hard,more

AUTHOR

Charles R Greathouse IV, Jun 21 2012

STATUS

approved

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Last modified June 25 17:47 EDT 2019. Contains 324353 sequences. (Running on oeis4.)