A116202 Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 8.

7, 54, 234, 267, 894, 58227, 7962242238271227055830015496107, 60153956829051761181170060654114714579377214308482459, 2019668016997743800626449453386765007975459365956534868322001037107, 3031524678136833532602149525055953135725227119574025423809994922862

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			58227//58233 = 76303 * 76311, where // denotes concatenation.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..16

Crossrefs

Cf. A116196, A116147, A116203, A116210, A116333.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116202_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(22,a,all_roots=True)):
            if a*(b-6) <= k**2-22 < a*(a-7) and k>4:
                yield (k**2-22)//a
A116202_list = list(islice(A116202_gen(),7)) # Chai Wah Wu, Feb 21 2024

Extensions

a(8)-a(10) from Chai Wah Wu, Feb 21 2024