A123034 Prime sums of 5 positive 5th powers.

5, 67, 1301, 1543, 2113, 2293, 2777, 3191, 3253, 3347, 3371, 3433, 3613, 4339, 5237, 5417, 5659, 6229, 6737, 7307, 7549, 7873, 8053, 8537, 8803, 9377, 9439, 9619, 9857, 10099, 11177, 11423, 11927, 12743, 15797, 15859, 16811, 17053, 17183, 18679, 18919, 19163

Offset

1,1

Comments

Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584}.

There must be an odd number of odd terms in the sum, either 5 odd terms (as with 5 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 and 16811 = 1^5 + 1^5 + 1^5 + 1^5 + 7^5), two even and 3 odd terms (as with 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 and 1301 = 1^5 + 1^5 + 2^5 + 3^5 + 4^5) or four even terms and one odd term (as with 3253 = 2^5 + 2^5 + 2^5 + 2^5 + 5^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

A000040 INTERSECTION A003350.

Example

a(1) = 5 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
a(2) = 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5.
a(3) = 1301 = 1^5 + 1^5 + 2^5 + 3^5 + 4^5.
a(4) = 1543 = 1^5 + 2^5 + 3^5 + 3^5 + 4^5.
a(5) = 2113 = 1^5 + 2^5 + 2^5 + 4^5 + 4^5.
a(6) = 3191 = 1^5 + 1^5 + 2^5 + 2^5 + 5^5.
a(7) = 4339 = 3^5 + 4^5 + 4^5 + 4^5 + 4^5.

Mathematica

Take[Select[Union[Total/@Tuples[Range[10]^5, 5]], PrimeQ], 60] (* Harvey P. Dale, Jul 21 2014 *)

Crossrefs

Cf. A000040, A000584, A003336, A003347, A003349, A003350.

Sequence in context: A316146 A113265 A124435 * A166619 A323208 A262656

Adjacent sequences: A123031 A123032 A123033 * A123035 A123036 A123037

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 24 2006

Extensions

Corrected and extended by Harvey P. Dale, Jul 21 2014

Status

approved