A343739 a(n) is the last digit to appear in sqrt(n) (or -1 if n is a square).

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

Offset

1,2

Comments

For the digit position in sqrt(n) at which the digit a(n) first appears, see A343740.

Links

Table of n, a(n) for n=1..84.

Formula

a(100^q*n) = a(n), q > 0. - Bernard Schott, Jul 24 2021

Example

a(2)=8 because 8 is the last digit to appear in sqrt(2) = 1.414213562373095048...;
a(24)=0 because 0 is the last digit to appear in sqrt(24) = 4.898979485566356196394568149411782783931894961313340...

Mathematica

Table[If[IntegerQ@ Sqrt@ n, -1, Function[s, FirstPosition[#, Max@ #][[1]] - 1 &@ Array[FirstPosition[s, #][[1]] &, 10, 0]]@ RealDigits[Sqrt[n], 10, 120][[1]]], {n, 84}] (* Michael De Vlieger, Jul 06 2021 *)

Prog

(Python 3.8+)
from math import isqrt
def A343739(n):
    i = isqrt(n)
    if i**2 == n:
        return -1
    m, dset = n, set()
    for d in (int(s) for s in str(i)):
        dset.add(d)
        if len(dset) == 10:
            return d
    while len(dset) < 10:
        m *= 100
        d = isqrt(m) % 10
        dset.add(d)
    return d # Chai Wah Wu, Jul 07 2021

Crossrefs

Cf. A023961, A343740, A343741, A343742.

Sequence in context: A011267 A049469 A349625 * A021547 A154527 A145435

Adjacent sequences: A343736 A343737 A343738 * A343740 A343741 A343742

Keyword

sign,base

Author

Jon E. Schoenfield, Jul 05 2021

Status

approved