A182479 Primes of the form p^2 + q^2 + r^2, where p,q,r are distinct primes.

83, 179, 227, 347, 419, 467, 491, 563, 587, 659, 827, 971, 1019, 1091, 1259, 1427, 1499, 1667, 1811, 1907, 1979, 2027, 2243, 2267, 2339, 2531, 2579, 2699, 2819, 2843, 2939, 3347, 3539, 3659, 3779, 3851, 4019, 4091, 4259, 4451, 4523, 4547, 4691, 4787, 5099

Offset

1,1

Comments

All terms are congruent to 5 modulo 6. Smallest of primes p, q, r is always 3. - Zak Seidov, Jun 03 2014

The number of such representations of a prime of that form is A263723. - Jonathan Sondow and Robert G. Wilson v, Nov 02 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

5099 = 3^2 + 7^2 + 71^2.

Mathematica

mx = 20; ps = Prime[Range[2, mx + 1]]; t = Table[ps[[i]]^2 + ps[[j]]^2 + ps[[k]]^2, {i, mx}, {j, i + 1, mx}, {k, j + 1, mx}]; Select[Union[Flatten[t]], # <= 34 + ps[[-1]]^2 && PrimeQ[#] &] (* T. D. Noe, May 01 2012 *)

Prog

(PARI) list(lim)=my(v=List(), t); lim\=1; forprime(p=7, sqrt(lim), forprime(q=5, min(sqrtint(lim-p^2-9), p-1), t=p^2+q^2; forprime(r=3, min(sqrtint(lim-t), q-1), if(isprime(t+r^2), listput(v, t+r^2))))); vecsort(Vec(v), , 8)
\\ Charles R Greathouse IV, May 01 2012

Crossrefs

Cf. A123592, A123597, A137365, A263723.

Cf. A137364 (the same with repetitions). - Zak Seidov, Jun 03 2014

Sequence in context: A111078 A106962 A137364 * A106094 A142443 A044415

Adjacent sequences: A182476 A182477 A182478 * A182480 A182481 A182482

Keyword

nonn

Author

Alex Ratushnyak, May 01 2012

Status

approved