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A066719
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Numbers n such that 1+n^phi(n) is prime.
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2
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OFFSET
| 1,2
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EXAMPLE
| 4^phi(4) + 1 = 4^2 + 1 = 17, a prime, so 4 is a term of the sequence.
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MATHEMATICA
| Do[s=1+n^(EulerPhi[n]); If[PrimeQ[s], Print[{n, s}]], {n, 1, 1000}]
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PROG
| (PARI) for(n=1, 6000, print(n); s=1+n^eulerphi(n); if(isprime(s), print(n, " ", s))) - Rick L. Shepherd Apr 03 2002
It suffices to search only even n - with, e.g. PARI forstep (n=6002, 7000, 2, ...) - because a(1)=1 is the only possible odd term. (Note that the average number of digits of s ( length(Str(s)) ) for the 500 even candidates from 6002 to 7000 is 10048 with a minimum of 5087 digits and a maximum of 13450 digits).
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CROSSREFS
| Cf. A067975, A000010.
Sequence in context: A009257 A098757 A056012 * A033319 A185151 A090315
Adjacent sequences: A066716 A066717 A066718 * A066720 A066721 A066722
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KEYWORD
| nonn,hard
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 14 2002
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EXTENSIONS
| Robert G. Wilson v reports no more primes up to 1400.
Any additional terms are larger than 6000. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Apr 03 2002
Edited by T. D. Noe (noe(AT)sspectra.com), Oct 30 2008
Further terms are greater than 10,000.
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