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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

Regarded as a decimal fraction, 0.01206932015794604621863800... is likely to be an irrational number.

Examples

			sqrt(0) = 0.0, so a(0) = 0 with the convention that the 0th digit after the decimal point is the digit before the decimal point,
sqrt(1) = 1.0, where the first digit after the decimal point is a(1) = 0,
sqrt(2) = 1.4142135..., where the 2nd decimal digit is a(2) = 1,
sqrt(3) = 1.7320508..., where the 3rd decimal digit is a(3) = 2,
sqrt(4) = 2.0000000..., where the 4th decimal digit is a(4) = 0,
sqrt(5) = 2.2360679..., where the 5th decimal digit is a(5) = 6,
sqrt(6) = 2.4494897..., where the 6th decimal digit is a(6) = 9, etc.
From _M. F. Hasler_, Jun 22 2024: (Start)
For the frequency of the respective digits among the first 10^k terms, we have:
  k :   0's    1's   2's    3's   4's   5's   6's   7's   8's   9's
----+---------------------------------------------------------------
  1 :     4,     1,    2,     1,    0,    0,    1,    0,    0,    1;
  2 :    22,     6,    9,    11,   12,    7,    8,    8,    9,    8;
  3 :   126,   106,  105,    94,   95,   90,   86,   96,   92,  110;
  4 :  1097,  1026, 1037,  1031,  984,  979, 1000,  956,  922,  968;
  5 : 10320, 10053, 9926, 10122, 9855, 9985, 9934, 9857, 9855, 10093. (End)
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A071901.

Programs

Mathematica

Join[{0}, Array[ Function[ n, RealDigits[ N[ Sqrt[ n ], n+6 ] ]// (#[ [ 1, #[ [ 2 ] ]+n ] ])& ], 110 ]]
Table[ Floor[ Mod[10^n*Sqrt[n], 10]], {n, 0, 104}] (* Robert G. Wilson v, Jun 17 2002 *)

PARI

A003076(n)=sqrtint(n*100^n)%10;
apply(A003076, [0..99]) \\ M. F. Hasler, Jun 22 2024

Formula

From M. F. Hasler, Jun 22 2024: (Start)

a(n) = A000196(n*100^n) % 10, where n % 10 = A010879(n) is the final digit of n.

a(n) = 0 for all n in A000290 (but not only those). This explains that the value 0 is slightly more frequent than the other values. (End)

Extensions

Extension and program from Olivier Gérard, Oct 15 1997