A116210 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 8.

73, 101, 466, 577, 913, 938, 1027699544347561123497066503878337002, 1043891904746431592729642732987859418, 1406975496023772119400647610836667853, 3905041089422306453928649115284570106, 4582028691256280367677282506239892877, 4616148891509946292221374856300250093

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			938//945 = 965 * 973, where // denotes concatenation.
		

Crossrefs

Cf. A116202, A116209, A116211, A116223, A116341.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116210_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(23,a,all_roots=True)):
            if a*(b-7) <= k**2-23 < a*(a-8) and k>4:
                yield (k**2-23)//a
A116210_list = list(islice(A116210_gen(),10)) # Chai Wah Wu, Feb 22 2024

Extensions

a(10)-a(12) from Chai Wah Wu, Feb 22 2024