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A123040 Prime sums of 12 positive 5th powers. 1
43, 167, 229, 347, 353, 409, 769, 1097, 1277, 1283, 1439, 1619, 1823, 1861, 1979, 2003, 2089, 2213, 2221, 2393, 2549, 2579, 2729, 2791, 2939, 2971, 3001, 3119, 3167, 3181, 3229, 3299, 3323, 3329, 3361, 3533, 3541, 3571, 3697, 3931, 4049, 4079, 4111, 4159, 4259 (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 + A000584 + A000584}. There must be an odd number of odd terms in the sum, either one even and eleven odd (as with 11 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 and 769 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5), three even and nine odd (as with 347 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5), five even and seven odd (as with 167 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 and 409 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5), seven even and 5 odd terms (as with 229 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5), nine even and 3 odd terms (as with 161341 = 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 11^5) or eleven even terms and one odd term (as with 353 = 1^ 5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5). The sum of two positive 5th powers (A003347), other than 2 = 1^5 + 1^5, cannot be prime.

LINKS

Matthew House, Table of n, a(n) for n = 1..10000

FORMULA

A000040 INTERSECTION A003357.

EXAMPLE

a(1) = 43 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5.

a(2) = 167 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.

a(3) = 229 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.

a(4) = 347 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 3^5.

a(5) = 353 = 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5.

a(6) = 409 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 2^5 + 2^5 + 2^5 + 2^5 + 3^5.

a(7) = 769 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 3^5.

MAPLE

N:= 10000: # to get all terms <= N

B:= {seq(i^5, i=1..floor(N^(1/5)))}:

B2:= select(`<=`, {seq(seq(b+c, b=B), c=B)}, N):

B4:= select(`<=`, {seq(seq(b+c, b=B2), c=B2)}, N):

B8:= select(`<=`, {seq(seq(b+c, b=B4), c=B4)}, N):

B12:= select(`<=`, {seq(seq(b+c, b=B4), c=B8)}, N):

sort(select(isprime, convert(B12, list))); # Robert Israel, Aug 10 2015

CROSSREFS

Cf. A000040, A000584, A003336, A003347, A003349, A003350, A003351, A003352, A003353, A003354, A003355, A003356, A003357.

Sequence in context: A078852 A078956 A206399 * A142016 A140640 A083357

Adjacent sequences:  A123037 A123038 A123039 * A123041 A123042 A123043

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Sep 24 2006

EXTENSIONS

More terms from Matthew House, Aug 10 2015

STATUS

approved

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Last modified February 20 06:45 EST 2018. Contains 299358 sequences. (Running on oeis4.)