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A123033
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Prime sums of 4 positive 5-th powers.
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OFFSET
| 1,1
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COMMENTS
| Primes in the sumset {A000584 + A000584 + A000584 + A000584}. There must be an odd number of odd cubes in the sum, either one even and 3 odd cubes (as with 1^5 + 1^5 + 2^5 + 3^5 and 761 = 2^5 + 3^5 + 3^5 + 3^5) or three even cubes and one odd cube (as with 97 = 1^5 + 2^5 + 2^5 + 2^5 and 3221 = 2^5 + 2^5 + 2^5 + 5^5). The sum of two positive 5-th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
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FORMULA
| A000040 INTERSECTION A003349.
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EXAMPLE
| a(1) = 97 = 1^5 + 2^5 + 2^5 + 2^5.
a(2) = 277 = 1^5 + 1^5 + 2^5 + 3^5.
a(3) = 761 = 2^5 + 3^5 + 3^5 + 3^5.
a(7) = 3221 = 2^5 + 2^5 + 2^5 + 5^5.
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CROSSREFS
| Cf. A000040, A000584, A003336, A003347, A003349.
Sequence in context: A142908 A006310 A141986 * A142008 A008873 A142455
Adjacent sequences: A123030 A123031 A123032 * A123034 A123035 A123036
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 24 2006
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