A116196 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 8.

68, 12585135, 17104748, 34388975, 41634068, 1100788419388203283323, 1415702077730399453204, 1615864923864298764860, 1993221328488651223275, 3064119854121476750348, 3576300448435797632079, 3890538749986876109435

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			41634068//41634073 = 64524463 * 64524471, where // denotes concatenation.
		

Crossrefs

Cf. A116189, A116195, A116197, A116202, A116327.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116196_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(21,a,all_roots=True)):
            if a*(b-5) <= k**2-21 < a*(a-6) and k>4:
                yield (k**2-21)//a
A116196_list = list(islice(A116196_gen(),10)) # Chai Wah Wu, Feb 21 2024