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

1,1

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A000312, A068145.

Sequence in context: A003190 A322451 A213792 * A270480 A229051 A006526

Adjacent sequences: A133660 A133661 A133662 * A133664 A133665 A133666

Keyword

nonn

Author

Jonathan Vos Post, Dec 28 2007

Status

approved