A123300 Prime sums of 14 positive 5th powers.

107, 293, 349, 653, 659, 839, 1013, 1019, 1223, 1279, 1409, 1559, 1583, 1621, 1801, 1831, 1949, 2011, 2129, 2153, 2309, 2333, 2339, 2347, 2371, 2551, 2699, 2707, 2731, 2879, 2917, 3083, 3121, 3169, 3191, 3301, 3331, 3449, 3457, 3511, 3541, 3659, 3691, 3761, 3847, 4019, 4027, 4051

Offset: 1

Author

Jonathan Vos Post, Sep 25 2006

Keywords

• easy
• nonn

Examples

			a(1) = 107 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5.
a(2) = 293 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
a(3) = 349 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5.
a(4) = 653 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5.
		

Links

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

Crossrefs

Cf. A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354, A003355, A003356, A003357, A123294-A123299.

Programs

Mathematica

up = 5000; q = Range[up^(1/5)]^5; a={0}; Do[b = Select[Union@ Flatten@ Table[e + a, {e, q}], # <= up &]; a = b, {k, 14}]; Select[a, PrimeQ] (* Giovanni Resta, Jun 12 2016 *)

Formula

A000040 INTERSECTION A123295.

Extensions

More terms from Harvey P. Dale, Jan 01 2015

4 missing terms from Giovanni Resta, Jun 12 2016