A071901 n-th decimal digit of the fractional part of the square root of the n-th prime.

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, 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, 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

Offset: 1

Author

Roger L. Bagula, Jun 12 2002

Keywords

• nonn
• base

Comments

Regarded as a decimal fraction, 0.4367216431388... is likely to be an irrational number.

Examples

			sqrt(2)=1.4142135... -> the 1st decimal digit is 4;
sqrt(3)=1.7320508... -> the 2nd decimal digit is 3;
sqrt(5)=2.2360679... -> the 3rd decimal digit is 6, etc.
		

References

• Bryan Birch, Mathematical Fallacies and Paradoxes, Dover 1982; suggested by pages 120,121 and 122

Crossrefs

Cf. A003076.

Programs

Maple

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

Mathematica

q[n_] := Mod[ Floor[10^n*Sqrt[ Prime[n]]], 10]; Table[ q[n], {n, 1, 105}]
Table[rd=RealDigits[N[Sqrt[Prime[n]],2*n]]; rd[[1,rd[[2]]+n]],{n,10000,100000,10000}] (* Zak Seidov, Nov 17 2009 *)
ndd[n_]:=Module[{rd=RealDigits[Sqrt[Prime[n]],10,Prime[n]]}, Drop[ rd[[1]], rd[[2]]][[n]]]; Array[ndd,110]

PARI

A071901(n) = {local(r,x,d);r=sqrtint(prime(n));x=100*(prime(n)-r^2);
for(digits=1, n, d=0; while((20*r+d)*d <= x, d++);
d--; /* while loop overshoots correct digit */
x=100*(x-(20*r+d)*d); r=10*r+d); d} \\ Michael B. Porter, Dec 11 2009

Formula

a(n) = floor(10^n*sqrt(prime(n)))-10*floor(10^(n-1)*sqrt(prime(n))).

Extensions

Edited by Robert G. Wilson v and Henry Bottomley, Jun 13 2002