1,1

Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584}. There must be an odd number of odd cubes 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 cubes (as with 311 = 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5), four even and 3 odd cubes (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 cubes and one odd cube (as with 193 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5). The sum of two positive 5-th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.

A000040 INTERSECTION A003352.

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.

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

Adjacent sequences: A123033 A123034 A123035 this_sequence A123037 A123038 A123039

Sequence in context: A002614 A095885 A134056 this_sequence A142011 A074224 A099601

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 24 2006