A066719 Numbers n such that 1+n^phi(n) is prime.

1, 2, 4, 6, 96

Offset

1,2

Links

Table of n, a(n) for n=1..5.

Example

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

Mathematica

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

Prog

(PARI) for(n=1, 6000, print(n); s=1+n^eulerphi(n); if(isprime(s), print(n, " ", s)))
/* 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). */
\\ Rick L. Shepherd, Apr 03 2002

Crossrefs

Cf. A067975, A000010.

Sequence in context: A335709 A056012 A259050 * A345269 A345092 A033319

Adjacent sequences: A066716 A066717 A066718 * A066720 A066721 A066722

Keyword

nonn,hard

Author

Joseph L. Pe, Jan 14 2002

Extensions

Robert G. Wilson v reports no more primes up to 1400.

Any additional terms are larger than 6000. - Rick L. Shepherd, Apr 03 2002

Edited by T. D. Noe, Oct 30 2008

Further terms are greater than 10,000.

Status

approved