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A123036
Prime sums of 7 positive 5th powers.
1
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
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 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Sep 24 2006
EXTENSIONS
More terms from Harvey P. Dale, May 08 2012
STATUS
approved