A137364 -id:A137364 - cp's OEIS frontend

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

Alex Ratushnyak, May 01 2012

nonn

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

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

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

Cf. A123592, A123597, A137365, A263723.

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

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 *)

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

A243342 Least prime p that is expressible as the sum of three distinct primes squared in exactly n ways.

Original entry on oeis.org

83, 419, 3779, 10739, 240899, 229979, 1180019, 369419, 36964859, 33670379, 13235699, 21899939, 412547339, 370247939, 467152019, 579994619

Offset: 1

Zak Seidov, Jun 03 2014

All terms are congruent to 5 modulo 6 since the first square must be 9.

			p = 83, {a,b,c} = {3,5,7}, 1 way
p = 419, {a,b,c} = {3,7,19}, {3,11,17}, 2 ways
p = 3779, {a,b,c} ={3,7,61}, {3,17,59}, {3,31,53}, 3 ways
p = 10739, {a,b,c} = {3,11,103}, {3,23,101}, {3,53,89}, {3,67,79}, 4 ways.

Cf. A137364, A182475, A182479.

p = a^2 + b^2 + c^2 with a < b < c primes, note that a = 3 in all cases.

cp's OEIS Frontend

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

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