A123036 Prime sums of 7 positive 5th powers.

7, 131, 193, 311, 373, 491, 733, 857, 1061, 1123, 1217, 1279, 1303, 1427, 1459, 1607, 1787, 2029, 2053, 2357, 3169, 3373, 3677, 3739, 3833, 3919, 4099, 4583, 5153, 5419, 5903, 6317, 6379, 6473, 7043, 7309, 7793, 7937, 8117, 8179, 8297, 8363, 8539, 8543, 8867

Offset: 1

Author

Jonathan Vos Post, Sep 24 2006

Keywords

• easy
• nonn

Comments

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

There must be an odd number of odd terms in the sum, either seven odd (as with 7 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5), two even and 5 odd terms (as with 311 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5), four even and 3 odd terms (as with 131 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 and 373 = 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5) or six even terms and one odd term (as with 193 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.

Examples

			a(1) = 7 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
a(2) = 131 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5.
a(3) = 193 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
a(4) = 311 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5.
a(5) = 373 = 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.
		

Links

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

Crossrefs

Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352.

Programs

Mathematica

Take[Union[Select[Total/@Tuples[Range[8]^5,7],PrimeQ]],50] (* Harvey P. Dale, May 08 2012 *)

Formula

A000040 INTERSECTION A003352.

Extensions

More terms from Harvey P. Dale, May 08 2012