A003076 -id:A003076 - cp's OEIS frontend

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

Roger L. Bagula, Jun 12 2002

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

			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.

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

Cf. A003076.

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

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]

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

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

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

A187765 The (n-1)th decimal place of the fractional part of the square root of n.

Original entry on oeis.org

0, 4, 3, 0, 0, 8, 1, 1, 0, 0, 3, 3, 3, 9, 1, 0, 5, 4, 2, 8, 8, 5, 4, 6, 0, 1, 2, 7, 5, 0, 8, 7, 2, 3, 0, 0, 2, 2, 7, 9, 4, 0, 6, 0, 7, 3, 0, 4, 0, 7, 3, 2, 4, 8, 8, 6, 9, 0, 7, 4, 3, 5, 7, 0, 2, 3, 3, 9, 8, 7, 5, 7, 9, 6, 4, 6, 3, 4, 9, 5, 0, 3, 5, 0, 7, 0, 2

Offset: 1

Ruskin Harding, Jan 04 2013

If n=1 then the term is the first digit before the decimal point. If the square root of n is a whole number then the term is 0.

			If n=2, sqrt(2)=1.41421356 approx., the 1st(2-1) decimal place of which is 4 so the 2nd term is 4. If n=3, sqrt(3)=1.73205081 approx., the 2nd(3-1) decimal place of which is 3 so the 3rd term is 3.

Cf. A003076 (n-th digit after decimal point of square root of n).

Join[{0}, Table[RealDigits[Sqrt[n] - Floor[Sqrt[n]], 10, n, -1][[1, -2]], {n, 2, 87}]]

for n in range(1,16):
    x=str(n**0.5)
    for i in range(n):
        x=x+"0"
    if n==1:
        r=str(x[-1])
    else:
        r=r+","+str(x[n])
    if n==15:
        print(r)

cp's OEIS Frontend

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

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