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 A123035 Prime sums of 6 positive 5th powers. 1
 37, 521, 1091, 1153, 1997, 2083, 2239, 3137, 3559, 4129, 4153, 4457, 4637, 5449, 6199, 7253, 8147, 8573, 9319, 9323, 10069, 10463, 11959, 14029, 15083, 15649, 16649, 16843, 16883, 17327, 17389, 17569, 17959, 18077, 18773, 18803, 19373, 20029 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes in the sumset {A000584 + A000584 + A000584 + A000584 + A000584 + A000584}. There must be an odd number of odd terms in the sum, either one even and 5 odd terms (as with 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5), three even and 3 odd terms (as with 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5) or five even terms and one odd term (as with 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5). 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 A003351. EXAMPLE a(1) = 37 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5. a(2) = 521 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5. a(3) = 1091 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 4^5. a(4) = 1153 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 4^5. 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, 6}]; Select[a, PrimeQ] (* Giovanni Resta, Jun 13 2016 *) CROSSREFS Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351. Sequence in context: A220331 A142764 A256811 * A232033 A006303 A219440 Adjacent sequences:  A123032 A123033 A123034 * A123036 A123037 A123038 KEYWORD nonn AUTHOR Jonathan Vos Post, Sep 24 2006 EXTENSIONS More terms from Max Alekseyev, Sep 24 2011 STATUS approved

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Last modified June 22 20:39 EDT 2021. Contains 345389 sequences. (Running on oeis4.)