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

1, 2, 4, 6, 96

Offset: 1

Author

Joseph L. Pe, Jan 14 2002

Keywords

• nonn
• hard
• more

Comments

Robert G. Wilson v reports no more primes up to 1400. - N. J. A. Sloane, Sep 22 2004

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

Further terms are greater than 10000. - Charles R Greathouse IV, Nov 23 2010

a(6) > 60000. - Michael S. Branicky, Apr 13 2025

Examples

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

Crossrefs

Cf. A067975, A000010.

Programs

Mathematica

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)))
/* 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

Extensions

Edited by T. D. Noe, Oct 30 2008