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%I #17 Apr 03 2023 10:36:10
%S 7,13,255,280,97241
%N Numbers k such that the first k digits of the Golden Ratio form a prime.
%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/">My Contributions in Prime Curios</a>
%H G. L. Honaker, Jr and Chris Caldwell, <a href="https://t5k.org/curios/page.php?number_id=1206">Prime Curios!</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConstantPrimes.html">Constant Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatioDigits.html">Golden Ratio Digits</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Phi-Prime.html">Phi-Prime</a>
%e a(1)=7 because the 7-digit number 1618033 is prime.
%t Do[If[PrimeQ[ FromDigits[RealDigits[N[GoldenRatio, n + 10], 10, n][[1]]]], Print[n]], {n, 1, 3000}]
%t With[{gr=RealDigits[GoldenRatio,10,100000][[1]]},Select[Range[ 100000], PrimeQ[ FromDigits[Take[gr,#]]]&]] (* _Harvey P. Dale_, Jul 24 2016 *)
%Y Cf. A064117.
%K base,hard,nonn
%O 1,1
%A _Shyam Sunder Gupta_, Sep 09 2001
%E a(5) = 97241 from _Eric W. Weisstein_, Jun 04 2009
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