A133663 Primes of the form a^a + b^b + c^c.

3, 29, 3637, 6277, 46687, 826669, 16777499, 16780597, 404197709, 775664521, 10000003129, 10387420493, 285311673737, 305311670611, 8916100448513, 8916487869001, 8926101271799, 17832200896513, 17832200899637

Offset: 1

Author

Jonathan Vos Post, Dec 28 2007

Keywords

• nonn

Examples

			a(1) = 3 = 1 + 1 + 1 is prime.
a(2) = 29 = 27 + 1 + 1 is prime.
a(3) = 3637 = 3125 + 256 + 256 is prime.
a(4) = 6277 = 3125 + 3125 + 27 is prime.
a(5) = 46687 = 46656 + 27 + 4 is prime.
a(6) = 826669 = 823543 + 3125 + 1 is prime.
a(7) = 16777499 = 16777216 + 256 + 27 is prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..7093

Crossrefs

Cf. A000040, A000312, A068145.

Programs

Mathematica

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

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

Formula

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