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Search: id:A075432
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| A075432 |
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Primes with no square-free neighbors. |
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+0
9
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| 17, 19, 53, 89, 97, 127, 149, 151, 163, 197, 199, 233, 241, 251, 269, 271, 293, 307, 337, 349, 379, 449, 487, 491, 521, 523, 557, 577, 593, 631, 701, 727, 739, 751, 773, 809, 811, 881, 883, 919
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Complement of A075430 in A000040.
I propose a shorter name: Non-Euclidean Primes. That is justified by the Euclid's demonstration of the infinitude of primes. It appears that the proportion of Non-Euclidean primes respect to primes tend to the limit 1/4. [From Ludovicus (luiroto(AT)yahoo.com), Nov 16 2009]
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EXAMPLE
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Neither neighbor of 19 is square-free: 19-1=18=2*3^2 and 19+1=20=5*2^2, therefore 19 is a term.
Example: Below 10000 there are 2380 Non-Euclidean and 9592 primes 2380/9592 = 0.248... [From Ludovicus (luiroto(AT)yahoo.com), Nov 16 2009]
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MATHEMATICA
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lst={}; Do[p=Prime[n]; If[ !SquareFreeQ[Floor[p-1]]&&!SquareFreeQ[Floor[p+1]], AppendTo[lst, p]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 20 2008]
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CROSSREFS
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Cf. A039787, A049097, A005117, A000040.
Sequence in context: A095081 A144709 A132239 this_sequence A119768 A005808 A028489
Adjacent sequences: A075429 A075430 A075431 this_sequence A075433 A075434 A075435
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KEYWORD
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nonn,new
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 15 2002
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