Search: id:A066719
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%I A066719
%S A066719 1,2,4,6,96
%N A066719 Numbers n such that 1+n^phi(n) is prime.
%e A066719 4^EulerPhi(4) + 1 = 4^2 + 1 = 17, a prime, so 4 is a term of the sequence.
%t A066719 Do[s=1+n^(EulerPhi[n]); If[PrimeQ[s], Print[{n, s}]], {n, 1, 1000}]
%o A066719 (PARI) for(n=1,6000,print(n); s=1+n^eulerphi(n); if(isprime(s),print(n,
               " ",s))) When it returns true (1), PARI's isprime used as above (with 
               default flag=0) only guarantees that s "passes the strong pseudoprime 
               test for 10 randomly chosen bases". - Rick L. Shepherd Apr 03 2002
%o A066719 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).
%Y A066719 Cf. A067975, A000010.
%Y A066719 Sequence in context: A009257 A098757 A056012 this_sequence A033319 A090315 
               A083753
%Y A066719 Adjacent sequences: A066716 A066717 A066718 this_sequence A066720 A066721 
               A066722
%K A066719 nonn
%O A066719 1,2
%A A066719 Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 14 2002
%E A066719 Robert G. Wilson v reports no more primes up to 1400.
%E A066719 Any additional terms are larger than 6000. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), 
               Apr 03 2002
%E A066719 Edited by T. D. Noe (noe(AT)sspectra.com), Oct 30 2008

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