OFFSET
1,1
EXAMPLE
Primes p=13, q=7, and r=11 give 13^2 + 1 = 7^2 + 11^2 = 170, so 13 + 7 + 11 = 31 (prime) is a term.
Primes p=17, q=11, and r=13 give 17^2 + 1 = 11^2 + 13^2 = 290, so 17 + 11 + 13 = 41 (prime) is a term.
Primes p=23, q=13, and r=19 give 23^2 + 1 = 13^2 + 19^2 = 530, but 23 + 13 + 19 = 55 (composite), so 55 is not a term.
Primes p=31, q=11, and r=29 give 31^2 + 1 = 11^2 + 29^2 = 962, so 31 + 11 + 29 = 71 (prime) is a term.
MAPLE
From Emeric Deutsch, Jun 21 2009: (Start)
The second Maple program yields the pairs [x+y+z, [x, y, z]].
A := {}: for i to 250 do for j to 250 do for k to 250 do x := ithprime(i): y := ithprime(j): z := ithprime(k): if `and`(isprime(x+y+z) = true, x^2+1 = y^2+z^2) then A := `union`(A, {x+y+z}) else end if end do end do end do: A; # end of the program
B := {}: for i to 20 do for j to 20 do for k to 20 do x := ithprime(i): y := ithprime(j): z := ithprime(k): if `and`(isprime(x+y+z) = true, x^2+1 = y^2+z^2) then B := `union`(B, {[x+y+z, [x, y, z]]}) else end if end do end do end do: B; # end of the program
(End)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladislav-Stepan Malakhovsky and Juri-Stepan Gerasimov, May 31 2009
EXTENSIONS
Corrected and extended by Emeric Deutsch, Jun 21 2009
Edited by Jon E. Schoenfield, Feb 23 2019
STATUS
approved