login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A160961
Primes of the form p + q + r with p, q and r also prime such that p^2 + 1 = q^2 + r^2.
0
17, 31, 41, 71, 89, 97, 109, 113, 127, 197, 239, 251, 349, 379, 433, 461, 631, 829, 881, 911, 919, 953, 967, 991, 1151, 1231, 1427, 1429, 1471, 1693, 1759, 1847, 1871, 2143, 2269, 2273, 2393, 2399, 2437, 2531, 2591, 2617, 2633, 2647, 2729, 2851, 2953, 2969
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
Cf. A000040.
Sequence in context: A134076 A258029 A321596 * A260805 A267781 A270441
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