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A122728
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Primes that are the sum of 4 positive cubes.
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0
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11, 37, 67, 89, 107, 137, 149, 163, 191, 193, 233, 271, 317, 353, 367, 379, 383, 409, 439, 461, 467, 479, 503, 523, 541, 587, 593, 601, 613, 631, 641, 653, 691, 709, 739, 751, 773, 809, 821, 839, 857, 863, 883, 887, 919, 929, 947, 971, 983, 991, 1033, 1069
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| By parity, there must be an odd number of odds in the sum. Hence this sequence is the union of primes which are the sum of the cube of an even number and the cubes of three odd numbers (such as 11 = 1^3 + 1^3 + 1^3 + 2^3) and the primes which are the sum of the cube of an odd number and the cubes of three even numbers (such as 149 = 2^3 + 2^3 + 2^3 + 5^3). A subset of this sequence is the primes which are the sum of the cubes of four distinct primes (i.e. of the form 2^3 + p^3 + q^3 + r^3 for p, q, r, distinct odd primes) such as 503 = 2^3 + 3^3 + 5^3 + 7^3; or 2357 = 2^3 + 3^3 + 5^3 + 13^3. No prime can be the sum of two cubes (by factorization of the sum of two cubes).
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FORMULA
| A000040 INTERSECTION A003327.
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EXAMPLE
| a(1) = 11 = 1^3 + 1^3 + 1^3 + 2^3.
a(2) = 37 = 1^3 + 1^3 + 2^3 + 3^3.
a(3) = 67 = 1^3 + 1^3 + 1^3 + 4^3.
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MATHEMATICA
| mx = 1000; lim = Floor[(mx - 3)^(1/3)]; Select[Union[Total /@ Tuples[Range[lim]^3, {4}]], # <= mx && PrimeQ[#] &] (* From Harvey P. Dale, May 25 2011 *)
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CROSSREFS
| Cf. A000040, A003327.
Sequence in context: A125744 A116057 A099227 * A031381 A160023 A188135
Adjacent sequences: A122725 A122726 A122727 * A122729 A122730 A122731
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 23 2006
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EXTENSIONS
| More terms from Harvey P. Dale, May 25 2011.
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