A123033 Prime sums of 4 positive 5th powers.

97, 277, 761, 1511, 1753, 2081, 3221, 3643, 6197, 7517, 7841, 8263, 10067, 10399, 10903, 16903, 25639, 32771, 32833, 33013, 33647, 33889, 35059, 36137, 39019, 40577, 40819, 48563, 49639, 57383, 59083, 59567, 60317, 61129, 62207, 63199, 66383, 66889, 100003

Offset

1,1

Comments

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

There must be an odd number of odd terms in the sum, either one even and 3 odd terms (as with 1^5 + 1^5 + 2^5 + 3^5 and 761 = 2^5 + 3^5 + 3^5 + 3^5) or three even terms and one odd term (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 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 A003349.

Example

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.

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, 4}]; Select[a, PrimeQ] (* Giovanni Resta, Jun 13 2016 *)

Crossrefs

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

Sequence in context: A142908 A006310 A141986 * A142008 A008873 A142455

Adjacent sequences: A123030 A123031 A123032 * A123034 A123035 A123036

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 24 2006

Extensions

More terms from Alois P. Heinz, Aug 12 2015

Status

approved