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Search: id:A164307
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OFFSET
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1,1
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COMMENT
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Primes of the form sum_{j=1..u} j^x for some x>0, u>1. (Since the case of x=1 leads to the triangular numbers with no
additional primes, this is equivalent to the definition.)
Primes in A000330 (x=2), or in A000537 (x=3), or in A000538 (x=4), or in A000539 (x=5) etc. See A164312 for the x.
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EXAMPLE
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1^1 + 2^1 = 3. 1^2 + 2^2 = 5. 1^4 + 2^4 = 17. 1^16 + 2^16 = 65537.
1^1440 + 2^1440 + 3^1440 + 4^1440 + 5^1440 = 3.287049497374559048967261852*10^1006 = 3287049497374559048967261852 ... 458593539025033893379.
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MATHEMATICA
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lst={}; Do[s=0; Do[If[PrimeQ[s+=n^x], AppendTo[lst, s]; Print[Date[], s]], {n, 4!}], {x, 7!}]; lst
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CROSSREFS
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Cf. A000215, A070592, A019434, A092506, A093179, A100270, A123599.
Sequence in context: A056130 A078726 A019434 this_sequence A125045 A093179 A067387
Adjacent sequences: A164304 A164305 A164306 this_sequence A164308 A164309 A164310
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KEYWORD
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nonn,more
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 12 2009
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2009
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