A133664 Primes of the form a^a + b^b + c^c + d^d.

7, 13, 59, 311, 337, 769, 3137, 3389, 9631, 46691, 49783, 49789, 139969, 143093, 823601, 826673, 826699, 870253, 916859, 16777729, 16780369, 16780601, 16823903, 16827001, 17600761, 17600813, 18427427, 33557561, 33604213, 34378231

Offset: 1

Author

Jonathan Vos Post, Dec 28 2007

Keywords

• easy
• nonn

Examples

			a(1) = 7 = 2^2 + 1^1 + 1^1 + 1^1 = 4 + 1 + 1 + 1 = 7.
a(2) = 13 = 4 + 4 + 4 + 1.
a(3) = 59 = 27 + 27 + 4 + 1.
a(4) = 311 = 256 + 27 + 27 + 1.
a(5) = 337 = 256 + 27 + 27 + 27.
a(6) = 769 = 256 + 256 + 256 + 1.
		

Links

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

Crossrefs

Cf. A000040, A000312, A068145.

Programs

Mathematica

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

PARI

v=[];for(a=1,100, for(b=1,a, for(c=1,b, for(d=1,c, if(ispseudoprime(t=a^a+b^b+c^c+d^d),v=concat(v,t)))))); v \\ Charles R Greathouse IV, Feb 15 2011

Formula

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