A065868 Initial n digits in decimal portion of golden ratio phi (or tau) = (1 + sqrt 5)/2 form a prime number.

2, 14, 887, 4267, 5163, 8867, 18644, 24429, 130911

Offset: 1

Author

Jason Earls, Dec 07 2001

Keywords

• base
• nonn

Comments

887 certified prime with Primo.

Note: the upper bound of 10^6 in this program has not actually been reached, so the next term may occur at any value >8867. - Ryan Propper, Aug 12 2005

Search limit is 200000. - Serge Batalov, Jun 21 2017

Crossrefs

Cf. A047658, A057563, A001622.

Programs

Mathematica

phi = First@ RealDigits[N[GoldenRatio - 1, 10^6 + 1]]; Do[k = FromDigits[Take[phi, n]]; If[PrimeQ[k], Print[n]], {n, 1, 10^6}] (* Ryan Propper, Aug 12 2005, edited by Michael De Vlieger, Jun 21 2017 *)

Extensions

a(4)-a(6) from Ryan Propper, Aug 12 2005

a(7)-a(9) from Serge Batalov, Jun 21 2017