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

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

1,2

Comments

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.

Links

Table of n, a(n) for n=1..87.

Example

If n=2, sqrt(2)=1.41421356..., the 1st (2-1) decimal place of which is 4 so the 2nd term is 4.
If n=3, sqrt(3)=1.73205080..., the 2nd (3-1) decimal place of which is 3 so the 3rd term is 3.

Mathematica

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

Prog

(Python)
from math import isqrt
def a(n):
    if n<2: return 0
    return isqrt(n*100**(n-1))%10
print([a(n) for n in range(1, 88)]) # Jason Yuen, Jan 10 2026

Crossrefs

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

Sequence in context: A257536 A019983 A019984 * A274818 A274819 A106646

Adjacent sequences: A187762 A187763 A187764 * A187766 A187767 A187768

Keyword

nonn,base

Author

Ruskin Harding, Jan 04 2013

Status

approved