A064119 Numbers k such that the first k digits of the Golden Ratio form a prime.

7, 13, 255, 280, 97241

Offset: 1

Author

Shyam Sunder Gupta, Sep 09 2001

Keywords

• base
• hard
• nonn

Examples

			a(1)=7 because the 7-digit number 1618033 is prime.
		

Links

• Shyam Sunder Gupta, My Contributions in Prime Curios
• G. L. Honaker, Jr and Chris Caldwell, Prime Curios!
• Eric Weisstein's World of Mathematics, Constant Primes
• Eric Weisstein's World of Mathematics, Golden Ratio Digits
• Eric Weisstein's World of Mathematics, Integer Sequence Primes
• Eric Weisstein's World of Mathematics, Phi-Prime

Crossrefs

Cf. A064117.

Programs

Mathematica

Do[If[PrimeQ[ FromDigits[RealDigits[N[GoldenRatio, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 3000}]
With[{gr=RealDigits[GoldenRatio,10,100000][[1]]},Select[Range[ 100000], PrimeQ[ FromDigits[Take[gr,#]]]&]] (* Harvey P. Dale, Jul 24 2016 *)

Extensions

a(5) = 97241 from Eric W. Weisstein, Jun 04 2009