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Search: id:A152913
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| A152913 |
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Primes of the form n^4+(n+1)^4. |
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1
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| 17, 97, 337, 881, 3697, 10657, 16561, 49297, 66977, 89041, 149057, 847601, 988417, 1146097, 1972097, 2522257, 2836961, 3553777, 3959297, 4398577, 5385761, 7166897, 11073217, 17653681, 32530177, 41532497, 44048497, 55272097, 61627201
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes in A008514.
Sequence is disjoint to A005385: If n^4+(n+1)^4 is a prime p, then (p-1)/2 = n^4 + 2*n^3 + 3*n^2 + 2*n. (p-1)/2 = 8 for n = 1 and (p-1)/2 is divisible by n for n > 1. In each case (p-1)/2 is not prime.
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EXAMPLE
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For n=3, n^4+(n+1)^4 = 337 is prime and (337-1)/2 = 168 = 3*56 is not prime.
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MATHEMATICA
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f[n_]:=n^4+(n+1)^4; lst={}; Do[a=f[n]; If[PrimeQ[a], AppendTo[lst, a]], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 30 2009]
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PROGRAM
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(MAGMA) [ a: n in [1..80] | IsPrime(a) where a is n^4+(n+1)^4 ];
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CROSSREFS
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Cf. A008514 (4-dimensional centered cube numbers), A005385 (safe primes p: (p-1)/2 is also prime).
Sequence in context: A103766 A165347 A008514 this_sequence A044268 A044649 A160827
Adjacent sequences: A152910 A152911 A152912 this_sequence A152914 A152915 A152916
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Dec 15 2008
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EXTENSIONS
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Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 21 2008
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