1,2

4^EulerPhi(4) + 1 = 4^2 + 1 = 17, a prime, so 4 is a term of the sequence.

Do[s=1+n^(EulerPhi[n]); If[PrimeQ[s], Print[{n, s}]], {n, 1, 1000}]

(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

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).

Cf. A067975, A000010.

Sequence in context: A009257 A098757 A056012 this_sequence A033319 A090315 A083753

Adjacent sequences: A066716 A066717 A066718 this_sequence A066720 A066721 A066722

nonn

Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Jan 14 2002

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