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A075432
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Primes with no squarefree neighbors.
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8
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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 1-2.A ; A= Artin's constant = .37395581... This table calculated by Jens K. Andersen corroborate it: 10^5: 2421 / 9592 = 0.2523978315 10^6: 19812 / 78498 = 0.2523885958 10^7: 167489 / 664579 = 0.2520227091 10^8: 1452678 / 5761455 = 0.2521373507 10^9: 12817966 / 50847534 = 0.2520862860 10^10: 114713084 / 455052511 = 0.2520875750 10^11: 1038117249 / 4118054813 = 0.2520892256 It comes close to the expected 1-2*C. From Ludovicus (luiroto(AT)yahoo.com), Dec. 07 2009. References: "Artin's Primitive Root Conjecture", Pieter Moree's ArXiv:math/0412262v1, "Conjecture 65", www.primepuzzles.net.
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MATHEMATICA
| 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
| Cf. A039787, A049097, A005117, A000040.
Sequence in context: A095081 A144709 A132239 * A119768 A005808 A180559
Adjacent sequences: A075429 A075430 A075431 * A075433 A075434 A075435
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KEYWORD
| nonn
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 15 2002
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