A116288 Numbers k such that k*(k+4) gives the concatenation of a number m with itself.

7, 97, 451, 546, 689, 854, 997, 4380, 5617, 9997, 72728, 99997, 346531, 653466, 999997, 9090906, 9999997, 94117644, 99999997, 334665331, 336032385, 378253326, 390977440, 439928489, 483516484, 516483513, 560071508

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Comments

Contains 10^m - 3 hence the sequence is infinite. - David A. Corneth, Feb 20 2024

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A116125, A116275, A116287, A116289, A116297.

Programs

Python

from itertools import count, islice
from sympy import sqrt_mod
def A116288_gen(): # generator of terms
    for j in count(0):
        b = 10**j
        a = b*10+1
        for k in sorted(sqrt_mod(4,a,all_roots=True)):
            if a*b <= k**2-4 < a*(a-1):
                yield k-2
A116288_list = list(islice(A116288_gen(),40)) # Chai Wah Wu, Feb 20 2024