1,1

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.

A000040 INTERSECTION A003349.

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.

Cf. A000040, A000584, A003336, A003347, A003349.

Sequence in context: A142908 A006310 A141986 this_sequence A142008 A008873 A142455

Adjacent sequences: A123030 A123031 A123032 this_sequence A123034 A123035 A123036

easy,nonn

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