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Search: id:A123039
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| A123039 |
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Prime sums of 11 positive 5-th powers. |
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1
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OFFSET
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1,1
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COMMENT
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Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584}. There must be an odd number of odd cubes in the sum, either eleven odd (as with 11 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5), two even and nine odd (as with 73 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 and 557 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5 + 3^5), four even and seven odd (as with 619 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5), six even and 5 odd cubes (as with 197 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 and 439 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5), eight even and 3 odd cubes (as with 743 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5) or ten even cubes and one odd cube (as with 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5). The sum of two positive 5-th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.
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FORMULA
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A000040 INTERSECTION A003356.
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EXAMPLE
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a(1) = 11 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
a(2) = 73 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5.
a(3) = 197 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.
a(4) = 439 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.
a(5) = 557 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5 + 3^5.
a(6) = 563 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.
a(7) = 619 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5.
a(8) = 743 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5.
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CROSSREFS
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Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354, A003355, A003356.
Sequence in context: A006975 A084900 A142015 this_sequence A092244 A054461 A003367
Adjacent sequences: A123036 A123037 A123038 this_sequence A123040 A123041 A123042
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 24 2006
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