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 nine odd (as with 251 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5 and 977 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5), two even and seven odd (as with 71 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 and 313 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5), four even and 5 odd cubes (as with xxxx), six even and 3 odd cubes (as with 3803 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 5^5) or eight even cubes and one odd cube (as with 257 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 and 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.

A000040 INTERSECTION A003354.

a(1) = 71 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5.

a(2) = 251 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5.

a(3) = 257 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.

a(4) = 313 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 3^5.

a(5) = 499 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5

a(9) = 977 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5.

Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354.

Sequence in context: A096698 A001126 A140628 this_sequence A142325 A142013 A033240

Adjacent sequences: A123035 A123036 A123037 this_sequence A123039 A123040 A123041

easy,nonn

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