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A123038 Prime sums of 9 positive 5th powers. 1
71, 251, 257, 313, 499, 617, 797, 859, 977, 1039, 1063, 1187, 1249, 1367, 1429, 1523, 1609, 1789, 1913, 2179, 2273, 2297, 2539, 2663, 2843, 3023, 3109, 3257, 3319, 3413, 3499, 3593, 3617, 3803, 4373, 4733, 4889, 5179, 5303, 5483, 5639, 5881, 6257, 6389, 6451 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

There must be an odd number of odd terms 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 terms (as with xxxx), six even and 3 odd terms (as with 3803 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 5^5) or eight even terms and one odd term (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 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 A003354.

EXAMPLE

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.

MATHEMATICA

up = 10^4; q = Range[up^(1/5)]^5; a = {0}; Do[b = Select[ Union@ Flatten@ Table[e + a, {e, q}], # <= up &]; a = b, {k, 9}]; Select[a, PrimeQ] (* Giovanni Resta, Jun 13 2016 *)

CROSSREFS

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

Sequence in context: A160369 A001126 A140628 * A325079 A142325 A232475

Adjacent sequences:  A123035 A123036 A123037 * A123039 A123040 A123041

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Sep 24 2006

EXTENSIONS

More terms from Alois P. Heinz, Aug 12 2015

STATUS

approved

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Last modified May 18 01:37 EDT 2021. Contains 343992 sequences. (Running on oeis4.)