

A066719


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


2




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: A098757 A056012 A259050 * A033319 A185151 A218087
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



