login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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