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

1,1

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.

Links

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

Formula

A000040 INTERSECTION A003352.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A361367 A332050 A134056 * A142011 A074224 A158701

Adjacent sequences: A123033 A123034 A123035 * A123037 A123038 A123039

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 24 2006

Extensions

More terms from Harvey P. Dale, May 08 2012

Status

approved