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Primes of the form a^a + b^b + c^c.
2

%I #9 May 13 2013 01:54:09

%S 3,29,3637,6277,46687,826669,16777499,16780597,404197709,775664521,

%T 10000003129,10387420493,285311673737,305311670611,8916100448513,

%U 8916487869001,8926101271799,17832200896513,17832200899637

%N Primes of the form a^a + b^b + c^c.

%H Charles R Greathouse IV, <a href="/A133663/b133663.txt">Table of n, a(n) for n = 1..7093</a>

%F A000040 INTERSECTION {A000312(i) + A000312(j) + A000312(k)}.

%e a(1) = 3 = 1 + 1 + 1 is prime.

%e a(2) = 29 = 27 + 1 + 1 is prime.

%e a(3) = 3637 = 3125 + 256 + 256 is prime.

%e a(4) = 6277 = 3125 + 3125 + 27 is prime.

%e a(5) = 46687 = 46656 + 27 + 4 is prime.

%e a(6) = 826669 = 823543 + 3125 + 1 is prime.

%e a(7) = 16777499 = 16777216 + 256 + 27 is prime.

%t Select[Union[ Flatten[Table[ a^a + b^b + c^c, {a, 1, 40}, {b, 1, a}, {c, 1, b}]]], PrimeQ]

%o (PARI) v=[];for(a=1,386, for(b=1,a, for(c=1,b, if(ispseudoprime(t=a^a+b^b+c^c),v=concat(v,t))))); v \\ _Charles R Greathouse IV_, Feb 18 2011

%Y Cf. A000040, A000312, A068145.

%K nonn

%O 1,1

%A _Jonathan Vos Post_, Dec 28 2007