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A123034 Prime sums of 5 positive 5th powers. 1
5, 67, 1301, 1543, 2113, 2293, 2777, 3191, 3253, 3347, 3371, 3433, 3613, 4339, 5237, 5417, 5659, 6229, 6737, 7307, 7549, 7873, 8053, 8537, 8803, 9377, 9439, 9619, 9857, 10099, 11177, 11423, 11927, 12743, 15797, 15859, 16811, 17053, 17183, 18679, 18919, 19163 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

There must be an odd number of odd terms in the sum, either 5 odd terms (as with 5 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 and 16811 = 1^5 + 1^5 + 1^5 + 1^5 + 7^5), two even and 3 odd terms (as with 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 and 1301 = 1^5 + 1^5 + 2^5 + 3^5 + 4^5) or four even terms and one odd term (as with 3253 = 2^5 + 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 A003350.

EXAMPLE

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

a(2) = 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5.

a(3) = 1301 = 1^5 + 1^5 + 2^5 + 3^5 + 4^5.

a(4) = 1543 = 1^5 + 2^5 + 3^5 + 3^5 + 4^5.

a(5) = 2113 = 1^5 + 2^5 + 2^5 + 4^5 + 4^5.

a(6) = 3191 = 1^5 + 1^5 + 2^5 + 2^5 + 5^5.

a(7) = 4339 = 3^5 + 4^5 + 4^5 + 4^5 + 4^5.

MATHEMATICA

Take[Select[Union[Total/@Tuples[Range[10]^5, 5]], PrimeQ], 60] (* Harvey P. Dale, Jul 21 2014 *)

CROSSREFS

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

Sequence in context: A316146 A113265 A124435 * A166619 A323208 A262656

Adjacent sequences:  A123031 A123032 A123033 * A123035 A123036 A123037

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Sep 24 2006

EXTENSIONS

Corrected and extended by Harvey P. Dale, Jul 21 2014

STATUS

approved

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Last modified August 12 15:13 EDT 2022. Contains 356077 sequences. (Running on oeis4.)