A071177 Square-root of concatenation n'k, where k is minimal with n'k square (decimal notation).

4, 5, 6, 7, 23, 8, 27, 9, 31, 10, 34, 11, 37, 12, 39, 13, 42, 43, 14, 45, 46, 15, 152, 156, 16, 162, 165, 17, 54, 55, 56, 18, 58, 59, 188, 19, 61, 62, 63, 20, 203, 65, 66, 21, 213, 68, 69, 22, 222, 71, 72, 23, 73, 74, 235, 75, 24, 242

Offset: 1

Author

Reinhard Zumkeller, May 15 2002

Keywords

• nonn
• base

Comments

a(n) = A000196(n'A071176(n))

Examples

			a(5) = 23 as 23^2 = 529 = 5'29 and 5'i is nonsquare for i<29, A071176(5)=29.
		

Programs

Python

from math import isqrt
def A071177(n):
    m = 10*n
    if (k:=isqrt(m))**2!=m:
        a = 1
        while (k:=isqrt(a*(m+1)-1)+1)**2-m*a>=10*a:
            a *= 10
    return k # Chai Wah Wu, Feb 15 2023