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%I #22 Nov 27 2015 15:22:33
%S 4,3,6,7,2,1,6,4,3,1,3,8,8,0,4,2,7,4,9,3,1,4,2,0,4,1,8,6,4,9,8,8,1,4,
%T 3,4,0,8,4,1,0,2,8,6,3,2,3,7,4,7,6,6,2,5,0,1,2,3,1,3,7,4,4,7,7,4,3,6,
%U 9,6,1,2,1,9,8,9,4,2,9,9,3,5,6,9,0,4,9,3,8,6,9,6,3,6,4,2,6,3,5,9,3,7,8,9,6
%N n-th decimal digit of the fractional part of the square root of the n-th prime.
%C Regarded as a decimal fraction, 0.4367216431388... is likely to be an irrational number.
%D Bryan Birch, Mathematical Fallacies and Paradoxes, Dover 1982; suggested by pages 120,121 and 122
%F a(n) = floor(10^n*sqrt(prime(n)))-10*floor(10^(n-1)*sqrt(prime(n))).
%e sqrt(2)=1.4142135... -> the 1st decimal digit is 4;
%e sqrt(3)=1.7320508... -> the 2nd decimal digit is 3;
%e sqrt(5)=2.2360679... -> the 3rd decimal digit is 6, etc.
%p A071901 := proc(n) local p; p := ithprime(n) ; Digits := p+3 ; floor(10^n*sqrt(p)) mod 10 ; end proc: seq(A071901(n),n=1..120) ; # _R. J. Mathar_, Nov 17 2009
%t q[n_] := Mod[ Floor[10^n*Sqrt[ Prime[n]]], 10]; Table[ q[n], {n, 1, 105}]
%t Table[rd=RealDigits[N[Sqrt[Prime[n]],2*n]]; rd[[1,rd[[2]]+n]],{n,10000,100000,10000}] (* _Zak Seidov_, Nov 17 2009 *)
%t ndd[n_]:=Module[{rd=RealDigits[Sqrt[Prime[n]],10,Prime[n]]}, Drop[ rd[[1]], rd[[2]]][[n]]]; Array[ndd,110]
%o (PARI) A071901(n) = {local(r,x,d);r=sqrtint(prime(n));x=100*(prime(n)-r^2);
%o for(digits=1, n, d=0; while((20*r+d)*d <= x, d++);
%o d--; /* while loop overshoots correct digit */
%o x=100*(x-(20*r+d)*d); r=10*r+d); d} \\ _Michael B. Porter_, Dec 11 2009
%Y Cf. A003076.
%K nonn,base
%O 1,1
%A _Roger L. Bagula_, Jun 12 2002
%E Edited by _Robert G. Wilson v_ and _Henry Bottomley_, Jun 13 2002
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