OFFSET
1,1
COMMENTS
Primes of the form (u^4 + v^4)/2 with u and v odd and (u^8 + 6*u^4*v^4 + v^8)/8 prime. - Robert Israel, Feb 24 2017
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) == 1 (mod 8).
a(n) == 1 or 33 (mod 40).
EXAMPLE
For prime 41 = 5^2 + 4^2 is 5^2 - 4^2 = 3^2 and 5^4 + 4^4 = 881 is prime.
MAPLE
N:= 10^7: # to get all terms <= N Res:= {}:
for w from 1 to floor((2*N)^(1/4)) by 2 do
for u from 1 to min(w-1, floor((2*N-w^4)^(1/4))) by 2 do
p:= (u^4 + w^4)/2;
if isprime(p) and isprime((u^8 + 6*u^4*w^4 + w^8)/8) then
Res:= Res union {p}
fi;
od od:
sort(convert(Res, list)); # Robert Israel, Feb 24 2017
MATHEMATICA
Select[Total[#^2]&/@Select[Subsets[Range[3000], {2}], IntegerQ[Sqrt[#[[2]]^2-#[[1]]^2]] && PrimeQ[ Total[#^4]]&], PrimeQ]//Union (* Harvey P. Dale, Jul 23 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski and Altug Alkan, Feb 23 2017
STATUS
approved