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

1,1

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

Prog

(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

Crossrefs

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

Sequence in context: A116125 A142315 A359637 * A219088 A116261 A289851

Adjacent sequences: A116285 A116286 A116287 * A116289 A116290 A116291

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Status

approved