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A123043 Prime sums of 10 positive 5th powers. 1
41, 103, 227, 283, 587, 829, 953, 1009, 1033, 1399, 1493, 1523, 1579, 1759, 2063, 2087, 2243, 2273, 2633, 2789, 2969, 3079, 3203, 3359, 3407, 3413, 3469, 3539, 3593, 3929, 4133, 4157, 4219, 4289, 4523, 4679, 4703, 5101, 5273, 5851, 6203, 6389, 6421, 6569, 6991 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

There must be an odd number of odd terms in the sum, either one even and nine odd (as with 41 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 283 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5), three even and seven odd (as with 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 and 587 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5), five even and 5 odd terms (as with 17939 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 7^5), seven even and 3 odd terms (as with 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5) or nine even terms and one odd term (as with 3413 = 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 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 A003355.

EXAMPLE

a(1) = 41 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5.

a(2) = 103 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5.

a(3) = 227 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.

a(4) = 283 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5.

a(5) = 587 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 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, 10}]; Select[a, PrimeQ] (* Giovanni Resta, Jun 13 2016 *)

CROSSREFS

Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354, A003355.

Sequence in context: A142794 A225888 A156971 * A142014 A115163 A044228

Adjacent sequences:  A123040 A123041 A123042 * A123044 A123045 A123046

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 March 5 11:57 EST 2021. Contains 341823 sequences. (Running on oeis4.)