1,1

Primes in the sumset {A000584 + A000584 + A000584}. There must be an odd number of odd cubes in the sum, either 3 odd cubes (as with 3 = 1^5 + 1^5 + 1^5 and 487 = 1^5 + 3^5 + 3^5 and 59051 = 1^5 + 1^5 + 9^5) or two even cubes and one odd cube (as with 307 = 2^5 + 2^5 + 3^5 and 9043 = 3^5 + 4^5 + 6^5). The sum of two positive 5-th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.

A000040 INTERSECTION A003336.

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

a(2) = 307 = 2^5 + 2^5 + 3^5.

a(3) = 487 = 1^5 + 3^5 + 3^5.

a(4) = 9043 = 3^5 + 4^5 + 6^5.

a(5) = 16871 = 2^5 + 2^5 + 7^5.

a(6) = 17293 = 3^5 + 3^5 + 7^5.

a(7) = 23057 = 5^5 + 5^5 + 7^5.

Cf. A000040, A000584, A003336, A003347.

Adjacent sequences: A123029 A123030 A123031 this_sequence A123033 A123034 A123035

Sequence in context: A052505 A071525 A085319 this_sequence A132305 A074327 A062333

easy,nonn

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