A065868 - OEIS

%I #23 Dec 15 2017 17:35:45

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

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

%C 887 certified prime with Primo.

%C 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

%C Search limit is 200000. - _Serge Batalov_, Jun 21 2017

%t 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 *)

%Y Cf. A047658, A057563, A001622.

%K base,nonn

%O 1,1

%A _Jason Earls_, Dec 07 2001

%E a(4)-a(6) from _Ryan Propper_, Aug 12 2005

%E a(7)-a(9) from _Serge Batalov_, Jun 21 2017