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A182479 Primes of the form p^2 + q^2 + r^2, where p,q,r are distinct primes. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 21 04:55 EST 2020. Contains 332086 sequences. (Running on oeis4.)