OFFSET
1,1
COMMENTS
Some terms may occur in more than one way (but are just listed once): for example, a(73)=137633 = 8^4+13^4+18^4 = 9^4+16^4+16^4 with 8^2+13^2+18^2 = 557 and 9^2+16^2+16^2 = 593. - Robert Israel, Oct 26 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
P1=a^4+b^4+c^4; P= a^2+b^2+c^2; P1 and P are primes; P1 > P
EXAMPLE
5393=1^4+6^4+8^4=1+1296+4096 and 101=1^2+6^2+8^2=1+36+64;
6833= 2^4+4^4+9^4 = 16+256+6561 and 101= 2^2+4^2+9^2 =4+16+81;
339690083=99^4 +103^4 +107^4=96059601+112550881+131079601 and
31859=99^2 +103^2 +107^2 =9801+10609+11499;
MAPLE
N:= 10^5: # for terms <= N
R:= {}:
for a from 1 to floor((N/3)^(1/4)) do
for b from a to floor(((N-a^4)/2)^(1/4)) do
for c from b to floor((N-a^4-b^4)^(1/4)) do
x:= a^4 + b^4 + c^4;
if x > 3 and isprime(x) and isprime(a^2+b^2+c^2) then
R:= R union {x};
fi
od od od:
sort(convert(R, list)); # Robert Israel, Oct 26 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Tomas Xordan, Mar 05 2007
EXTENSIONS
Corrected by Robert Israel, Oct 26 2020
STATUS
approved