%I #8 Dec 07 2022 16:50:52
%S 6,1,0,3,7,9,8,8,5,3,5,7,3,9,8,8,4,8,5,4,2,2,7,2,1,4,4,0,8,3,3,2,9,1,
%T 7,6,4,9,5,5,6,8,9,8,2,7,6,6,0,2,0,2,9,3,4,7,2,0,5,9,4,1,9,0,4,7,5,8,
%U 4,2,5,0,1,0,8,4,2,7,8,6,0,9,2,0,1,1,0,1,1,7,6,8,5,6,7,3,3,8,3,9,7,7,1,2,0
%N a(n) = pth digit of phi where p = nth prime.
%C The primeth digits of Phi.
%C Is the number 6.10379885357398... irrational, transcendental?
%e The 5th prime is 11. The 11th digit of Phi is 7, the 5th term in the sequence.
%t With[{nn=600},Pick[RealDigits[GoldenRatio,10,nn][[1]],If[PrimeQ[#],1,0]&/@Range[nn],1]] (* _Harvey P. Dale_, Apr 22 2012 *)
%t Module[{nn=110,gr},gr=RealDigits[GoldenRatio,10,Prime[nn]][[1]];Table[gr[[p]],{p,Prime[ Range[nn]]}]] (* _Harvey P. Dale_, Dec 07 2022 *)
%o (PARI) \primeth.gp primeth(n) = { default(realprecision,1000); p=Str((sqrt(5)+1)/2*10^999); default(realprecision,28); forprime(x=2,n, print1(mid(p,x,1)",") ) } mid(str,s,n) = { v =""; tmp = Vec(str); ln=length(tmp); for(x=s,s+n1, v=concat(v,tmp[x]); ); return(v) }
%K base,easy,nonn
%O 2,1
%A _Cino Hilliard_, Jan 22 2004
