1,1

Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584 + A000584}. There must be an odd number of odd cubes in the sum, either one even and seven odd (as with 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 and 523 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5), three even and 5 odd cubes (as with 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5), five even and 3 odd cubes (as with 647 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5) or seven even cubes and one odd cube (as with 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.

A000040 INTERSECTION A003353.

a(1) = 101 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5.

a(2) = 163 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.

a(3) = 281 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5.

a(4) = 467 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.

a(5) = 523 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5.

a(6) = 647 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5.

Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353.

Sequence in context: A141927 A107186 A142660 this_sequence A142012 A067860 A140037

Adjacent sequences: A123034 A123035 A123036 this_sequence A123038 A123039 A123040

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 24 2006