A123035 Prime sums of 6 positive 5th powers.

37, 521, 1091, 1153, 1997, 2083, 2239, 3137, 3559, 4129, 4153, 4457, 4637, 5449, 6199, 7253, 8147, 8573, 9319, 9323, 10069, 10463, 11959, 14029, 15083, 15649, 16649, 16843, 16883, 17327, 17389, 17569, 17959, 18077, 18773, 18803, 19373, 20029

Offset

1,1

Comments

Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584}.

There must be an odd number of odd terms in the sum, either one even and 5 odd terms (as with 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5), three even and 3 odd terms (as with 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5) or five even terms and one odd term (as with 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

A000040 INTERSECTION A003351.

Example

a(1) = 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5.
a(2) = 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5.
a(3) = 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5.
a(4) = 1153 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5.

Mathematica

up = 10^6; q = Range[up^(1/5)]^5; a = {0}; Do[b = Select[ Union@ Flatten@Table[e + a, {e, q}], # <= up &]; a = b, {k, 6}]; Select[a, PrimeQ] (* Giovanni Resta, Jun 13 2016 *)

Crossrefs

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

Sequence in context: A220331 A142764 A256811 * A232033 A006303 A219440

Adjacent sequences: A123032 A123033 A123034 * A123036 A123037 A123038

Keyword

nonn

Author

Jonathan Vos Post, Sep 24 2006

Extensions

More terms from Max Alekseyev, Sep 24 2011

Status

approved