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

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

Offset: 1

Author

Zak Seidov, Jun 03 2014

Keywords

• nonn
• more

Comments

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

Examples

			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.
		

Crossrefs

Cf. A137364, A182475, A182479.

Formula

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