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A123033 Prime sums of 4 positive 5th powers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 10 20:21 EDT 2022. Contains 356039 sequences. (Running on oeis4.)