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 A126117 Primes p of the form a^4+b^4+c^4 with a,b,c>=1 such that a^2+b^2+c^2 is another prime < p. 1

%I

%S 83,113,163,353,593,787,1553,2593,3217,5393,6563,6833,7187,7793,8273,

%T 8963,9043,11953,14177,14723,16193,17123,20753,21283,21377,23603,

%U 25457,26561,27763,28643,29363,31153,35393,45233,46273,50593,50627,51137,52177,56113,57203,59233,61553,65267,65633,65713

%N Primes p of the form a^4+b^4+c^4 with a,b,c>=1 such that a^2+b^2+c^2 is another prime < p.

%C 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

%H Robert Israel, <a href="/A126117/b126117.txt">Table of n, a(n) for n = 1..10000</a>

%F P1=a^4+b^4+c^4; P= a^2+b^2+c^2; P1 and P are primes; P1 > P

%e 5393=1^4+6^4+8^4=1+1296+4096 and 101=1^2+6^2+8^2=1+36+64;

%e 6833= 2^4+4^4+9^4 = 16+256+6561 and 101= 2^2+4^2+9^2 =4+16+81;

%e 339690083=99^4 +103^4 +107^4=96059601+112550881+131079601 and

%e 31859=99^2 +103^2 +107^2 =9801+10609+11499;

%p N:= 10^5: # for terms <= N

%p R:= {}:

%p for a from 1 to floor((N/3)^(1/4)) do

%p for b from a to floor(((N-a^4)/2)^(1/4)) do

%p for c from b to floor((N-a^4-b^4)^(1/4)) do

%p x:= a^4 + b^4 + c^4;

%p if x > 3 and isprime(x) and isprime(a^2+b^2+c^2) then

%p R:= R union {x};

%p fi

%p od od od:

%p sort(convert(R,list)); # _Robert Israel_, Oct 26 2020

%K nonn

%O 1,1

%A _Tomas Xordan_, Mar 05 2007

%E Corrected by _Robert Israel_, Oct 26 2020

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Last modified December 2 08:31 EST 2021. Contains 349437 sequences. (Running on oeis4.)