A136292 Primes of the form a^a + b^b + c^c + d^d + e^e.

5, 11, 17, 31, 37, 43, 83, 89, 109, 263, 269, 521, 541, 547, 593, 773, 1051, 3181, 3187, 3413, 3691, 6763, 9377, 9403, 9887, 12527, 46663, 46993, 49787, 50549, 52937, 53189, 93851, 96697, 99563, 139999, 823547, 823553, 823573, 823651, 823831

Offset: 1

Author

Jonathan Vos Post, Apr 11 2008

Keywords

• easy
• nonn

Examples

			a(1) = 5 = 1^1 + 1^1 + 1^1 + 1^1 + 1^1.
a(2) = 11 = 1^1 + 1^1 + 1^1 + 2^2 + 2^2.
a(3) = 17 = 1^1 + 2^2 + 2^2 + 2^2 + 2^2.
a(4) = 31 = 1^1 + 1^1 + 1^1 + 1^1 + 3^3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000312, A068145, A133664.

Programs

Mathematica

Select[Union[ Flatten[Table[ a^a + b^b + c^c + d^d + e^e, {a, 1, 20}, {b, 1, a}, {c, 1, b}, {d, 1, c}, {e, 1, d}]]], PrimeQ]

PARI

v=[];for(a=1,50, for(b=1,a, for(c=1,b, for(d=1,c, for(e=1,d, if(ispseudoprime(t=a^a+b^b+c^c+d^d+e^e),v=concat(v,t))))))); v \\ Charles R Greathouse IV, Feb 15 2011

Formula

A000040 INTERSECTION {A000312(a) + A000312(b) + A000312(c) + A000312(d) + A000312(e)}.